Multi-fractal heatsink system and method

ABSTRACT

A heat sink comprising a heat exchange device having a large-scale morphology over a scale range and a small-scale texture over a scale range, wherein at least one of the large-scale morphology and the small scale texture has a fractal-like self-similarity over a scale range. The large-scale morphology and small-scale texture may be defined and implemented independently, or be provided with a transitional range. The large-scale morphology may be algorithmically optimized according to a set of geometrically constraints. The small-scale texture may be optimized according to aerodynamic parameters and constraints. The heat sink may be dynamically varying, and/or operated in conjunction with a dynamically varying heat transfer medium supply.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a Continuation of U.S. patent Ser. No.16/038,150, filed Jul. 17, 2018, now U.S. Pat. No. 11,031,312, issuedJun. 8, 2021, which claims benefit of priority from U.S. ProvisionalPatent Application Ser. No. 62/533,421, filed Jul. 17, 2017, theentirety of which is expressly incorporated herein by reference.

This application is also related to U.S. Patent Application Nos.61/331,103, filed May 4, 2010, Ser. No. 13/106,640, filed May 12, 2011,Ser. No. 14/817,962, filed Aug. 4, 2015, Ser. No. 14/984,756, filed Dec.30, 2015, Ser. No. 15/205,906, filed Jul. 8, 2016, 62/361,253, filedJul. 12, 2016, and Ser. No. 15/648,065, filed Jul. 12, 2017, each ofwhich is expressly incorporated herein by reference in its entirety.

FIELD OF THE INVENTION

This invention relates to the field of heat sinks or devices thattransfer heat between a heat source and a fluid, and more particularlyto heat sink designs exploiting fractal geometry principles.

BACKGROUND OF THE INVENTION

All references cited herein are expressly incorporated by reference intheir entirety, for their respective teachings regarding elements knownin the art, as if explicitly recited herein fully. These teachingsrepresent features and description of the invention, and are intended tosupport the description of the invention in various combinations,permutations, and subcombinations. It is noted that, in general, thereferences are applied to support the improvement of the heat sinktechnology discussed herein. In other cases, the technology hereof isemployed to improve the systems and methods set forth in theincorporated references, whether or not these represent heat sinktechnologies. In particular, references for various shapes andconfigurations include all such shapes described, in addition to thoseenumerated.

A heat sink is a term for a component or assembly that transfers heatgenerated within a solid material to a fluid (gas or liquid) medium,such as air or a cooling liquid. A heat sink is typically designed toincrease the surface area in contact with the cooling fluid or gassurrounding it, such as the air. Approach air velocity, choice ofmaterial, fin (or other protrusion) design and surface treatment aresome of the design factors which influence the thermal resistance, i.e.,thermal performance, of a heat sink. See,en.wikipedia.org/wiki/Heat_sink.

Heat sinks operate by removing heat from an object to be cooled into thesurrounding air, gas or liquid through convection and radiation.Convection occurs when heat is either carried passively from one pointto another by fluid motion (forced convection) or when heat itselfcauses fluid motion (free convection). When forced convection and freeconvection occur together, the process is termed mixed convection.Radiation occurs when energy, for example in the form of heat, travelsthrough a medium or through space and is ultimately absorbed by anotherbody. Thermal radiation is the process by which the surface of an objectradiates its thermal energy in the form of electromagnetic waves.Infrared radiation from a common household radiator or electric heateris an example of thermal radiation, as is the heat and light (IR andvisible EM waves) emitted by a glowing incandescent light bulb. Thermalradiation is generated when heat from the movement of charged particleswithin atoms is converted to electromagnetic radiation.

Heat transfer is the exchange of thermal energy between physicalsystems. The rate of heat transfer is dependent on the temperatures ofthe systems and the properties and states of the intervening mediumthrough which the heat is transferred. The three fundamental modes ofheat transfer are conduction, convection, and radiation. Heat transfer,the flow of energy in the form of heat, is a process by which a systemchanges its internal energy. The direction of heat transfer is from aregion of high temperature to a region of lower temperature, and isgoverned by the Second Law of Thermodynamics. Heat transfer changes theinternal energy of the respective systems, and occurs in a directionthat increases the entropy of the collection of systems. Thermalequilibrium is reached when all involved bodies and the surroundingsreach the same temperature. Thermodynamic and mechanical heat transferis calculated with the heat transfer coefficient, the proportionalitybetween the heat flux and the thermodynamic driving force for the flowof heat. See, Daniel Arovas, Lecture Notes on Thermodynamics andStatistical Mechanics (A Work in Progress), Department of Physics,University of California, San Diego, Nov. 14, 2013.

The fundamental modes of heat transfer are: Advection (the transportmechanism of a fluid from one location to another, and is dependent onmotion and momentum of that fluid); Conduction or diffusion (thetransfer of energy between objects that are in physical contact);Convection (The transfer of energy between an object and itsenvironment, due to fluid motion); and Radiation (The transfer of energyby the emission of electromagnetic radiation in the infrared part of thespectrum).

Heat conduction occurs as hot, rapidly moving or vibrating atoms andmolecules interact with neighboring atoms and molecules, transferringsome of their energy (heat) to these neighboring particles. Conductiontends to be the most significant means of heat transfer within a solidor between solid objects in thermal contact. Heat transfer between theheat source and heat sink, as well as through the heat sink, areconductive transfer. Advection operates by transferring matter with itsthermal energy, over space. Convective heat transfer, or convection, isthe transfer of heat from one place to another by the movement offluids, a process that is essentially the transfer of heat via masstransfer, and usually combines effects of heat conduction within thefluid (diffusion) and heat transference by bulk fluid flow streaming.

Convective cooling is sometimes described as Newton's law of cooling:The rate of heat loss of a body is proportional to the temperaturedifference between the body and its surroundings. Convective coolingdeviates from this “law”, and is not linearly dependent on temperaturegradients, and in some cases is strongly nonlinear.

Radiance or spectral radiance is a measure of the quantity of radiationthat passes through or is emitted. Radiant barriers are materials thatreflect radiation, and therefore reduce the flow of heat from radiationsources. The effectiveness of a radiant barrier is indicated by itsreflectivity, which is the fraction of radiation reflected. A materialwith a high reflectivity (at a given wavelength) has a low emissivity(at that same wavelength), and vice versa. At any specific wavelength,reflectivity=1−emissivity.

A heat sink tends to decrease the maximum temperature of the exposedsurface, because the power is transferred to a larger volume. This leadsto a possibility of diminishing return on larger heat sinks, since theradiative and convective dissipation tends to be related to thetemperature differential between the heat sink surface and the externalmedium. Therefore, if the heat sink is oversized, the efficiency of heatshedding is poor. If the heat sink is undersized, the object may beinsufficiently cooled, the surface of the heat sink dangerously hot, andthe heat shedding not much greater than the object itself absent theheat sink.

A heat sink transfers thermal energy from a higher temperature to alower temperature fluid or gas medium, by a process such as radiation,convection, and diffusion. The fluid medium is frequently air, but canalso be water or in the case of heat exchangers, oil, and refrigerants.Fourier's law of heat conduction, simplified to a one-dimensional formin the direction x, shows that when there is a temperature gradient in abody, heat will be transferred from the higher temperature region to thelower temperature region. The rate at which heat is transferred byconduction, q_(k), is proportional to the product of the temperaturegradient and the cross-sectional area through which heat is transferred:

$\begin{matrix}{q_{k} = {kA\frac{dT}{dx}}} & (1)\end{matrix}$

where q_(k) is the rate of conduction, k is a constant which depends onthe heat-conducting material, A is the surface area through which theheat is conducted, and dT/dx is the temperature gradient, i.e., the rateof change of temperature with respect to distance (for simplicity, theequation is written in one dimension). Thus, according to Fourier's law(which is not the only consideration by any means), heat sinks benefitfrom having a large surface area exposed to the medium into which theheat is to be transferred.

When dust settles on a heat sink, the area changes (typically increases,but by coating a microstructured surface, the area may decrease), andthe constant k will typically decrease, since the dust is not anoptimized heat transfer material, and often is a heat insulatingmaterial. The result is significant loss of heat sink efficiency. Thetendency of a surface to accumulate dust is therefore a factor in itsefficient use as a heat transfer surface with respect to a flowingmedium.

Consider a heat sink in a duct, where air flows through the duct, andthe heat sink base is higher in temperature than the air.

Fourier's law of heat conduction, simplified to a one-dimensional formin the x-direction, shows that when there is a temperature gradient in abody, heat will be transferred from the higher temperature region to thelower temperature region. Assuming conservation of energy, forsteady-state conditions, and applying the convection-cooling law, alsoknown as the Newton's law of cooling, gives the following set ofequations.

$\begin{matrix}{{\overset{˙}{Q} = {\overset{˙}{m}{c_{p,{in}}\left( {T_{{air},{out}} - T_{{air},{in}}} \right)}}},{\overset{˙}{Q} = \frac{T_{hs} - T_{{air},{av}}}{R_{hs}}},{{{where}T_{{air},{av}}} = \frac{T_{{air},{out}} + T_{{air},{in}}}{2}},} & {(2),(3),(4)}\end{matrix}$

and {dot over (Q)} is the first derivative of the thermal energy overtime

${- \overset{˙}{Q}} = {\frac{dQ}{dt}.}$

Using the mean air temperature is an assumption that is valid forrelatively short heat sinks. When compact heat exchangers arecalculated, the logarithmic mean air temperature is used. {dot over (m)}is the first derivative of mass over time, i.e., the air mass flow ratein kg/s.

The above equations show that when the airflow through or around theheat sink decreases, this results in an increase in the average airtemperature. This in turn increases the heat sink base temperature. Andadditionally, the thermal resistance of the heat sink will alsoincrease. The net result is a higher heat sink base temperature. Theinlet air temperature relates strongly with the heat sink basetemperature. Therefore, if there is no air or fluid flow around the heatsink, the energy dissipated to the air cannot be transferred to theambient air. Therefore, the heat sink functions poorly.

The fractal or branching architecture may be compelled by the thermaltransfer design, or other design constraint. For example, a fractalantenna may also serve as a heat sink, with the fractal features notcritically optimized as comparted to other designs with respect to heatshedding.

See, Casanova, Joaquin J., Jason A. Taylor, and Jenshan Lin. “Design ofa 3-D fractal heat sink antenna.” Antennas and Wireless PropagationLetters, IEEE 9 (2010): 1061-1064.

See also, Dannelley, Daniel. Enhancement of extended surface heattransfer using fractal-like geometries. Diss. The University of AlabamaTUSCALOOSA, 2013; and

Lee, S. R., Li, Z. G., Wang, B. G., Chiou, H. S., 2005, “An Applicationof the Fractal Theory in the Design of Heat Sink for PrecisionMeasurement Instrument,” Key Engineering Materials, 295-296, pp.717-722.

If a heat sink is initially optimized, the accretion of dust at thesurface will de-optimize the air flows and heat conductivity of heatsink fins, and also decrease efficiency on that basis. On the otherhand, the surface may be optimized to efficiently operate over a rangeof dust conditions, such that the clean surface is not necessarily thedesign target. Various methods have been proposed for removing dust fromheat sink fins, including vibration. See, U.S. 20070058346; 20080121373;20080121374; 20090272404; U.S. Pat. Nos. 6,544,309; 5,566,377;8,203,840; 8,400,766), air jets, and the like. See also, U.S. Pat. No.6,679,272; US20060260638; WO2008086479A2; US 20130206165; U.S. Pat. Nos.6,276,370; 7,614,406; 7,238,085; 5,834,871; US 20050003737; U.S. Pat.No. 6,002,588; US 20080017219; US 20130312787; US 20050003737.

In a heat sink shedding heat to a flowing medium, assuming that thelocal energy released and acoustic emissions are insignificant withrespect to the shed heat load, a local turbulence will increase the heattransfer efficiency. See,thermal.ferrotec.com/technology/thermoelectric-reference-guide/thermalref05/;www.thermalsoftware.com/optimum_sink_fan.pdf. Dust accumulation canincrease local turbulence, and in turbulent flow zones, the dustaccumulation may not be uniform.

A heat sink may have impaired efficiency when: (a) pin fins have a lotof surface area, but the pins are so close together that air has a hardtime flowing through them; (b) aligning a heat sink so that the fins arenot in the direction of flow; (c) aligning the fins horizontally for anatural convection heat sink. Whilst a heat sink is stationary and thereare no centrifugal forces and artificial gravity, air that is warmerthan the ambient temperature always flows upward, givenessentially-still-air surroundings; this is convective cooling.

The most common heat sink material is aluminum. Chemically pure aluminumis not used in the manufacture of heat sinks, but rather alloysen.wikipedia.org/wiki/Aluminium alloys. Aluminum alloy 1050A has one ofthe higher thermal conductivity values at 229 W/m·K. However, it is notrecommended for machining, since it is a relatively soft material.Aluminum alloys 6061 and 6063 are the more commonly used aluminumalloys, with thermal conductivity values of 166 and 201 W/m·K,respectively. The aforementioned values are dependent on the temper ofthe alloy. Copper is also used since it has around twice theconductivity of aluminum, but is three times as heavy as aluminum.Copper is also around four to six times more expensive than aluminum,but this is market dependent. Aluminum has the added advantage that itis able to be extruded, while copper cannot. Copper heat sinks aremachined and skived. Another method of manufacture is to solder the finsinto the heat sink base. Diamond is another possible heat sink material,typically limited in use by cost and fabrication issues. With a thermalconductivity value of 2000 W/m·K, it exceeds that of copper by a factorof five. In contrast to metals, where heat is conducted by delocalizedelectrons, lattice vibrations are responsible for diamond's very highthermal conductivity. For thermal management applications, theoutstanding thermal conductivity and diffusivity of diamond areessential. CVD diamond may be used as a sub-mount for high-powerintegrated circuits and laser diodes.

Composite materials also can be used. Examples are a copper-tungstenpseudoalloy en.wikipedia.org/wiki/Copper-tungsten, AlSiC(Silicon-Carbide in aluminum matrix, en.wikipedia.org/wiki/AlSiC,Dymalloy (diamond in copper-silver alloy matrix,en.wikipedia.org/wiki/Dymalloy), and E-material (beryllium oxideparticles in a beryllium matrix, hen.wikipedia.org/wiki/E-Material).Such materials are often used as substrates for chips, as their thermalexpansion coefficient can be matched to ceramics and semiconductors.

Fin efficiency is one of the parameters which make a higher thermalconductivity material important. A fin of a heat sink may be consideredto be a flat plate with heat flowing in one end and being dissipatedinto the surrounding fluid as it travels to the other. As heat flowsthrough the fin, the combination of the thermal resistance of the heatsink impeding the flow and the heat lost due to convection, thetemperature of the fin and, therefore, the heat transfer to the fluid,will decrease from the base to the end of the fin. This factor is calledthe fin efficiency and is defined as the actual heat transferred by thefin, divided by the heat transfer were the fin to be isothermal(hypothetically the fin having infinite thermal conductivity). Equations5 and 6 are applicable for straight fins.

$\begin{matrix}{{\eta_{f} = \frac{\tanh\left( {mL_{c}} \right)}{mL_{c}}},{{mL_{c}} = \sqrt{\frac{2h_{f}}{kt_{f}}L_{f}}}} & {(5),(6)}\end{matrix}$

Where h_(f) is the heat transfer coefficient(en.wikipedia.org/wiki/Heat_transfer_coefficient) of the fin (Air: 10 to100 W/(m²·K) Water: 500 to 10,000 W/(m²·K); k is the thermalconductivity (en.wikipedia.org/wiki/Thermal_conductivity) of the finmaterial (Aluminum: 120 to 240 Watt/m²K)); L_(f) is the fin height (m);and t_(f) is the fin thickness (m).

Another parameter that concerns the thermal conductivity of the heatsink material is spreading resistance. Spreading resistance occurs whenthermal energy is transferred from a small area to a larger area in asubstance with finite thermal conductivity. In a heat sink, this meansthat heat does not distribute uniformly through the heat sink base. Thespreading resistance phenomenon is shown by how the heat travels fromthe heat source location and causes a large temperature gradient betweenthe heat source and the edges of the heat sink. This means that somefins are at a lower temperature than if the heat source were uniformacross the base of the heat sink. This non-uniformity increases the heatsink's effective thermal resistance.

A pin fin heat sink is a heat sink that has pins that extend from itsbase. The pins can be, for example, cylindrical, elliptical orsquare/geometric polygonal. A second type of heat sink fin arrangementis the straight fin. These run the entire length of the heat sink. Avariation on the straight fin heat sink is a cross-cut heat sink. Astraight fin heat sink is cut at regular intervals but at a coarserpitch than a pin fin type.

In general, heat sink performance is correlated with surface area.However, this is not always true, since the actual heat dissipation isinfluenced by thermal gradients and convective flow, each of which isindependent of surface area per se. The concept of a pin fin heat sinkis to try to pack as much surface area into a given volume as possible,and often has low orientation dependence. (Because of convective flow,orientation with respect to the gravitational vector is often an issuein heat sinks).

T. Kordyban, “Hot air rises and heat sinks—Everything you know aboutcooling electronics is wrong”, ASME Press, N Y 1998 compares performanceof a pin fin and a straight fin heat sink of similar dimensions.Although the pin fin has 194 cm² surface area while the straight fin has58 cm², the temperature difference between the heat sink base and theambient air for the pin fin is 50° C. For the straight fin it was 44° C.or 6° C. better than the pin fin. Pin fin heat sink performance issignificantly better than straight fins where the fluid flows axiallyalong the pins rather than only tangentially across the pins.

Another configuration is the flared fin heat sink; its fins are notparallel to each other, but rather diverge with increasing distance fromthe base. Flaring the fins decreases flow resistance and makes more airgo through the heat sink fin channel; otherwise, more air would bypassthe fins. Slanting them keeps the overall dimensions the same, butoffers longer fins. Forghan, et al. have published data on testsconducted on pin fin, straight fin and flared fin heat sinks. See,Forghan, F., Goldthwaite, D., Ulinski, M., Metghalchi, M., Experimentaland Theoretical Investigation of Thermal Performance of Heat Sinks,ISME, May. 2001. They found that for low approach air velocity,typically around 1 m/s, the thermal performance is at least 20% betterthan straight fin heat sinks. Lasance and Eggink also found that for thebypass configurations that they tested, the flared heat sink performedbetter than the other heat sinks tested. See, Lasance, C. J. M andEggink, H. J., A Method to Rank Heat Sinks in Practice: The Heat SinkPerformance Tester, 21st IEEE SEMI-THERM Symposium 2001.

The heat transfer from the heat sink is mediated by two effects:conduction via the coolant, and thermal radiation. The surface of theheat sink influences its emissivity; shiny metal absorbs and radiatesonly a small amount of heat, while matte black is a good radiator. Incoolant-mediated heat transfer, the contribution of radiation isgenerally small. A layer of coating on the heat sink can then becounterproductive, as its thermal resistance can impair heat flow fromthe fins to the coolant. Finned heat sinks with convective or forcedflow will not benefit significantly from being colored. In situationswith significant contribution of radiative cooling, e.g., in case of aflat non-finned panel acting as a heat sink with low airflow, the heatsink surface finish can play an important role. Matte-black surfaceswill radiate much more efficiently than shiny bare metal. The importanceof radiative vs. coolant-mediated heat transfer increases in situationswith low ambient air pressure (e.g., high-altitude operations) or invacuum (e.g., satellites in space).

See, Fourier, J. B., 1822, Theorie analytique de la chaleur, Paris;Freeman, A., 1955, translation, Dover Publications, Inc., NY;

Kordyban, T., “Hot air rises and heat sinks—Everything you know aboutcooling electronics is wrong”, ASME Press, N Y 1998;

Bandon Munis, “Heat Sink Selection”, Thermal Management of Electronics,Mechanical Engineering Department, San Jose State University [Aug. 6,2006],www.sjsu.edu/people/nicole.okamoto/courses/me_146/Heat%20Sink.ppt;

portal.unimap.edu.my/portal/page/portal30/Lecturer%20Notes/kejuruteraan_mikroelektronik/semester%202%20sidang%20akademik%2020132014/emt%20230%20thermodynamics%20in%20electronic1/chapter%207%20thermal%20management%20heat%20sink.ppt;

Sergent, J. and Krum, A., 1998, Thermal management handbook forelectronic assemblies, First Edition, McGraw-Hill;

Incropera, F. P. and DeWitt, D. P., 1985, Introduction to heat transfer,John Wiley and sons, NY;

Forghan, Fariborz, Donald Goldthwaite, Matthew Ulinski, and HameedMetghalchi. “Experimental and theoretical investigation of thermalperformance of heat sinks.” In annual meeting for ISME, United States,May. 2001;

Lasance, C. J. M and Eggink, H. J., 2001, A Method to Rank Heat Sinks inPractice: The Heat Sink Performance Tester, 21st IEEE SEMI-THERMSymposium; ludens.cl/Electron/Thermal.html; Lienard, J. H., IV & V,2004, A Heat Transfer Textbook, Third edition, MIT;

Saint-Gobain, 2004, 22 Jul. 2008assets.sealanddesign.com/files/thermacool-brochure.pdf;

Jeggels, Y. U., Dobson, R. T., Jeggels, D. H., Comparison of the coolingperformance between heat pipe and aluminium conductors for electronicequipment enclosures, Proceedings of the 14th International Heat PipeConference, Florianopolis, Brazil, 2007;

Prstic, S., Iyengar, M., and Bar-Cohen, A., 2000, Bypass effect in highperformance heat sinks, Proceedings of the International Thermal ScienceSeminar Bled, Slovenia, June 11-14; Mills, A. F., 1999, Heat transfer,Second edition, Prentice Hall;

Potter, C. M. and Wiggert, D. C., 2002, Mechanics of fluid, ThirdEdition, Brooks/Cole;

White, F. M., 1999, Fluid mechanics, Fourth edition, McGraw-HillInternational;

Azar, A, et al., 2009, Qpedia Thermal E-Magazine, January 2009 Issue;www.qats.com/cpanel/UploadedPdf/January20092.pdf.

Several structurally complex heat sink designs are discussed in Hernon,US App. 2009/0321045.

The relationship between resistance to air flow and convection in heatsinks is discussed by Frigus Primore in “A Method for Comparing HeatSinks Based on Reynolds Analogy,” available atakemalhammar.fr/downloads/Reynolds_analogy_heat sinks.PDF. This articlenotes that for, plates, parallel plates, and cylinders to be cooled, itis necessary for the velocity of the surrounding fluid to be low inorder to minimize mechanical power losses. However, larger surface flowvelocities will increase the heat transfer efficiency, especially wherethe flow near the surface is turbulent, and substantially disrupts astagnant surface boundary layer. Primore also discusses heat sink finshapes and notes that no fin shape offers any heat dissipation or weightadvantage compared with planar fins, and that straight fins minimizepressure losses while maximizing heat flow. Therefore, the art generallyteaches that generally flat and planar surfaces are appropriate for mostheat sinks.

Frigus Primore, “Natural Convection and Inclined Parallel Plates,”www.engineeringclicks.com/natural-convection-and-inclined-parallel-plates/,discusses the use of natural convection (i.e., convection due to thethermal expansion of a gas surrounding a solid heat sink in normaloperating conditions) to cool electronics. One of the design goals ofvarious heat sinks is to increase the rate of natural convection, andusing parallel plates often attains this result. Parallel plate heatsinks are traditionally considered the most efficient and attempts todefine the optimal spacing and angle (relative to the direction of thefluid flow) of the heat sinks according to the equations in FIG. 1 :

Optimum Plate Spacing

$\begin{matrix}{{S_{opt} = {{k_{S} \cdot \left( \frac{L}{dT} \right)^{0.25}}{\cos(\gamma)}^{- 0.25}}}{\gamma_{opt} = {{a\tan\left( {\frac{1}{3}\frac{H}{W}} \right)\frac{H}{W}} < \sqrt{3}}}{\gamma_{opt} = {{\frac{\pi}{4} - {{0.5}08\left( \frac{H}{W} \right)^{- 1.237}\frac{H}{W}}} > \sqrt{3}}}} & (1)\end{matrix}$

Total heat Dissipation

$\begin{matrix}{{\overset{˙}{Q} = {k_{v} \cdot k_{\gamma} \cdot A_{c} \cdot H^{0.5} \cdot {dT}^{1.5}}}{k_{\gamma} = {{\sqrt{1 + {\frac{1}{9}\left( \frac{H}{W} \right)^{2}}}\frac{H}{W}} < \sqrt{3}}}{k_{\gamma} = {{{{0.3}{07 \cdot \left( \frac{H}{W} \right)^{- 0.5}}} + {{0.6}{96 \cdot \left( \frac{H}{W} \right)^{- {0.5}}}\frac{H}{W}}} > \sqrt{3}}}} & (2)\end{matrix}$

Applied Equation{dot over (Q)}=η _(v) ·k _(v) ·k _(γ) ·A _(c) ·H ^(0.5) ·dT _(ref)^(1.5);dT=Temperature difference (K)A _(c) =W·Dη_(v)=Volumetric efficiency[--]{dot over (Q)}=Heat dissipation[W]  (3)

“Natural Convection and Chimneys,” available atakemalhammar.fr/articels2/parallel_pl_Inc.html, Frigus Primore discussesthe use of parallel plates in chimney heat sinks. One purpose of thistype of design is to combine more efficient natural convection with achimney. Primore notes that the design suffers if there is laminar flow(which creates a re-circulation region in the fluid outlet, therebycompletely eliminating the benefit of the chimney) but benefits if thereis turbulent flow which allows heat to travel from the parallel platesinto the chimney and surrounding fluid.

Batten, Paul, et al. “Sub-Grid Turbulence Modeling for Unsteady Flowwith Acoustic Resonance,” available atwww.researchgate.net/publication/269068673_Sub-grid_turbulence_modeling_for_unsteady_flow_with_acoustic_resonance,discuss that when a fluid is flowing around an obstacle, localizedgeometric features, such as concave regions or cavities, create pocketsof separated flow which can generate self-sustaining oscillations andacoustic resonance. The concave regions or cavities serve tosubstantially reduce narrow band acoustic resonance as compared to flatsurfaces. This is beneficial to a heat sink in a turbulent flowenvironment because it allows for the reduction of oscillations andacoustic resonance, and therefore for an increase in the energyavailable for heat transfer.

Liu, S., et al., “Heat Transfer and Pressure Drop in FractalMicrochannel Heat Sink for Cooling of Electronic Chips,” 44 Heat MassTransfer 221 (2007), discuss a heat sink with a “fractal-like branchingflow network.” Liu's heat sink includes channels through which fluidswould flow in order to exchange heat with the heat sink.

Y. J. Lee, “Enhanced Microchannel Heat Sinks Using Oblique Fins,” IPACK2009-89059, similarly discusses a heat sink comprising a “fractal-shapedmicrochannel based on the fractal pattern of mammalian circulatory andrespiratory system.” Lee's idea, similar to that of Liu, is that therewould be channels inside the heat sink through which a fluid could flowto exchange heat with the heat sink. The stated improvement in Lee'sheat sink is (1) the disruption of the thermal boundary layerdevelopment; and (2) the generation of secondary flows.

Pence, D. V., 2002, “Reduced Pumping Power and Wall Temperature inMicrochannel Heat Sinks with Fractal-like Branching Channel Networks”,Microscale Thermophys. Eng. 5, pp. 293-311, mentions heat sinks thathave fractal-like channels allowing fluid to enter into the heat sink.The described advantage of Pence's structure is increased exposure ofthe heat sink to the fluid and lower pressure drops of the fluid whilein the heat sink.

In general, a properly designed heat sink system will take advantage ofthermally induced convection or forced air (e.g., a fan). In general, aturbulent flow near the surface of the heat sink disturbs a stagnantsurface layer, and improves performance. In many cases, the heat sinkoperates in a non-ideal environment subject to dust or oil; therefore,the heat sink design must accommodate the typical operating conditions,in addition to the as-manufactured state.

Therefore, two factors appear to conflict in optimizing theconfiguration of an external heat sink: the surface configurationdesigned to disturb laminar flow patterns, create turbulence, andenhance convective heat transfer, and the desire to efficiently flowlarge volumes of heat transfer fluid (e.g., air), over the surfaces,which is enhanced by laminar (smooth) flow. Even in passive dissipativedevice, convective flow may be a significant factor, and reducing airflow volume and velocity by increasing the effective impedance can becounterproductive. On the other hand, in some cases, the amount ofenergy necessary to move the air is dwarfed by the problem to be solved.In many computing systems, the processors are thermally constrained,that is, the functioning of the processor is limited by the ability toshed heat. In such cases, innovative ways to improve the efficiency ofheat transfer may yield significant benefit, even if in some regimes ofoperation, they impose certain inefficiencies.

Prior art heat sink designs have traditionally concentrated on geometrythat is Euclidian, involving structures such as the pin fins, straightfins, and flares discussed above.

N J Ryan, D A Stone, “Application of the FD-TD method to modelling theelectromagnetic radiation from heat sinks”, IEEE InternationalConference on Electromagnetic Compatibility, 1997. 10th (1-3 Sep. 1997),pp: 119-124, discloses a fractal antenna which also serves as a heatsink in a radio frequency transmitter.

Lance Covert, Jenshan Lin, Dan Janning, Thomas Dalrymple, “5.8 GHzorientation-specific extruded-fin heat sink antennas for 3D RF systemintegration”, 23 Apr. 2008 DOI: 10.1002/mop.23478, Microwave and OpticalTechnology Letters Volume 50, Issue 7, pages 1826-1831, July 2008 alsoprovide a heat sink which can be used as an antenna.

Wang, Chien-Chang, Chen-I. Hung, and Wei-Hsin Chen. “Design of heat sinkfor improving the performance of thermoelectric generator usingtwo-stage optimization.” Energy 39, no. 1 (2012): 236-245 addressvarious design parameters of a heat sink for dissipating heat from athermoelectric module.

See also Ledezma, G., Al M. Morega, and A. Bejan. “Optimal spacingbetween pin fins with impinging flow.” Journal of heat transfer 118, no.3 (1996): 570-577;

Kobus, C. J., and T. Oshio. “Development of a theoretical model forpredicting the thermal performance characteristics of a vertical pin-finarray heat sink under combined forced and natural convection withimpinging flow.” International Journal of heat and mass transfer 48, no.6 (2005): 1053-1063;

Khan, W. A., J. R. Culham, and M. M. Yovanovich. “Optimization ofpin-fin heat sinks using entropy generation minimization.” In Thermaland Thermomechanical Phenomena in Electronic Systems, 2004. ITHERM'04.The Ninth Intersociety Conference on, vol. 1, pp. 259-267. IEEE, 2004;

Duan, Zhipeng, and Y. S. Muzychka. “Experimental investigation of heattransfer in impingement air cooled plate fin heat sinks.” Journal ofelectronic packaging 128, no. 4 (2006): 412-418;

Kobus, C. J., and T. Oshio. “Predicting the thermal performancecharacteristics of staggered vertical pin fin array heat sinks undercombined mode radiation and mixed convection with impinging flow.”International Journal of Heat and Mass Transfer 48, no. 13 (2005):2684-2696;

Yu, Enchao, and Yogendra Joshi. “Heat transfer enhancement from encloseddiscrete components using pin-fin heat sinks.” International Journal ofHeat and Mass Transfer 45, no. 25 (2002): 4957-4966;

Yu, Xiaoling, Jianmei Feng, Quanke Feng, and Qiuwang Wang. “Developmentof a plate-pin fin heat sink and its performance comparisons with aplate fin heat sink.” Applied thermal engineering 25, no. 2-3 (2005):173-182;

Huang, Cheng-Hung, Jon-Jer Lu, and Herchang Ay. “A three-dimensionalheat sink module design problem with experimental verification.”International Journal of Heat and Mass Transfer 54, no. 7-8 (2011):1482-1492;

Li, Hung-Yi, Ming-Hung Chiang, and Kuan-Ying Chen. “Performance analysisof pin-fin heat sinks with confined impingement cooling.” IEEEtransactions on components and packaging technologies 30, no. 3 (2007):383-389;

Zhao, Z., and C. T. Avedisian. “Enhancing forced air convection heattransfer from an array of parallel plate fins using a heat pipe.”International journal of heat and mass transfer 40, no. 13 (1997):3135-3147;

Khan, Waqar Ahmed, J. Richard Culham, and M. Michael Yovanovich.“Modeling of cylindrical pin-fin heat sinks for electronic packaging.”IEEE Transactions On Components And Packaging Technologies: APublication Of The Ieee Components, Packaging, And ManufacturingTechnology Society 31, no. 3 (2008): 536;

Peles, Yoav, Ali Koşar, Chandan Mishra, Chih-Jung Kuo, and BrandonSchneider. “Forced convective heat transfer across a pin fin micro heatsink.” International Journal of Heat and Mass Transfer 48, no. 17(2005): 3615-3627;

Furukawa, Takahiro, and Wen-Jei Yang. “Reliability of heat sinkoptimization using entropy generation minimization.” In 8th AIAA/ASMEJoint Thermophysics and Heat Transfer Conference, p. 3216. 2002.

Li, Hung-Yi, Shung-Ming Chao, and Go-Long Tsai. “Thermal performancemeasurement of heat sinks with confined impinging jet by infraredthermography.” International Journal of Heat and Mass Transfer 48, no.25-26 (2005): 5386-5394 discusses use of infrared thermography to assessheat sink performance. According to the present technology, this may beused for real-time feedback and adaptive air flow control, e.g., nozzlepositioning and air flow control. Indeed, while typically, the mostefficient cooling will result from directing the air flow toward a hotspot, this is not necessarily the case, since the air flow effects arenon-linear and interactive with other parameters. Therefore, amultiobjective optimization may be employed. Kanyakam, Siwadol, andSujin Bureerat. “Multiobjective evolutionary optimization of splayedpin-fin heat sink.” Engineering Applications of Computational FluidMechanics 5, no. 4 (2011): 553-565.

Perforations in heat sink fins are known. See, Shaeri, M. R., M.Yaghoubi, and K. Jafarpur. “Heat transfer analysis of lateral perforatedfin heat sinks.” Applied energy 86, no. 10 (2009): 2019-2029.

See, U.S. 20140098542; 20130309778; 20130286666; 20130155687;20130042893; 20120174650; 20120031272; 20110280019; 20110226460;20090045967; 20090021270; 20070041159; 20060072289; U.S. Pat. Nos.8,784,540; 8,764,243; 8,602,599; 8,539,840; 8,506,674; 8,491,683;7,696,890; 7,113,402; and 5,856,836.

SUMMARY OF THE INVENTION

In a preferred embodiment, a heat sink employed according to the presenttechnology provides a branched network of elements. The networkbranching may be according to a fractal pattern, or have affine orself-similar characteristics at various scales. For example, there maybe three levels within a hierarchy with two intervening branch points,e.g., a single base, with 2-4 first level branches, 4-16 second levelbranches and, possibly, 8-32 third level branches. The branching patternmay be uniform or non-uniform/asymmetric. For example, a branching nodelocation and characteristics may be dependent on prior branching and aheat flow. The space-filling pattern may be defined based on variousspatial characteristics and constraints.

In other cases, the structure is expressed in terms of iterations of aniterated function system, which may produce a structure which is notbranched per se. See, en.wikipedia.org/wiki/Iterated_function_system.

For example, in a computer system, a power supply with a fan may belocated near the heat sink. It will therefore create an environmentalasymmetry, to which the design of the heat sink may respond. Likewise,the heat sink may be within a physical enclosure, and may have anasymmetric ventilation path, all leading to an asymmetric optimizeddesign for the external heat sink shape and characteristics. Further,the branching itself may be asymmetric, such that a larger portion ofthe heat flow is transmitted down a larger branch, while a smallerportion is transmitted down a narrower branch. However, due to geometry,the ratio of surface area (˜2πr) to cross section area (˜πr²)≈(2/r) issmaller for the larger branch than the smaller one, leading to a greaterheat dissipation efficiency for the smaller branch, just distal to thebranching point, than the larger branch. Meanwhile, the larger branchmore efficiently carries the heat load away from the branching point,and thus reduces competition for convective heat loss near the branchingpoint with respect to a narrower branch. Therefore, a fractal design,with asymmetric branching, can optimize the heat dissipation of the heatsink over space. Further, because the branching may be definedalgorithmically, the various environmental and spatial factors may allplay a role in an iterative optimized design, herein referred to as afractal heat sink.

According to the present technology, a fractal device is used to enhanceheat transfer from a heat sink, as compared to a heat sink structurewhich seeks to maintain laminar flows, such as a parallel plate heatsink. According to a preferred embodiment the fractal nature is observedat two difference scale ranges, though, as discussed above, theturbulent flow heat transfer medium may interact with a non-fractalstructure.

The large-scale optimization may have distinct operating regimes fromthe small scale or texture scale, making the implementation of a singleoptimization algorithm challenging and, possibility, difficult tomanufacture. The present technology may provide a second scale ofoptimization, addressing e.g., the surface configuration, such astexture, perforations, and micro-aerodynamic features. These texturescale features may also be of a fractal nature. The texture-scaleoptimization may involve features represented only within a single ortwo levels of size scale, though the underlying optimization may involvea higher number of iterations. Typically, the various fractal geometrieswill have different Hausdorff (fractal) dimensions.

While the two regimes may be provided with a smooth transition, it isalso possible to provide an arbitrary or manufacturing-feasibilitydriven transition between the two different schemes of optimization. Ofcourse, the composite heat sink may be modelled and optimized in toto,with modifications made to the design as may be appropriate.

The use of two (or more) different schemes (or algorithms) ofoptimization, both of which may be fractal/affine in nature (resultingin two or more fractal geometries with different Hausdorff dimensions),is referred to herein as a doubly-fractal or multi-fractal design. It isnoted that the technology is not limited to designs in which each scaleof optimization is per se fractal, and as such, one or both scale offeatures may be symmetric or non-iteratively defined, without departingfrom the essential elements of the technology.

In general, the optimal high-level features, e.g., the branch point andbranching ratios, proceed from a unitary base of the heat sink, whilethe optimal low-level features, e.g., textures, proceed from thegeometric boundaries of the terminal surfaces of the high levelfeatures.

When considered in a three-dimensional space, with a flow of a heattransfer medium about the surfaces of the heat sink, a fractal (roughlyself-similar over a range of scales) configuration can be implementedwhich optimizes for flow resistance, heat transfer efficiency, peaktemperatures, acoustic emissions as a function of frequency, mass and/orcost of materials, predicted dust accumulation/cleanliness afterextended operation (and self-cleaning efficiency), and other factors.The efficiency of heat transfer is dependent on various factors, such astemperature differential; therefore, one design aspect seeks to shed themost heat near the heat source (typically the base of the heat sink),and thus the thermal transfer medium flow rate may be highest at thatregion, with a high efficiency heat transfer material providing the heatflow path from the source to the shedding surface. On the other hand, atthe margins of the device, the thermal differentials will be low, andtherefore a higher surface area with lower flow rates may be moreoptimal. The high surface area may correspond to a region of reducedheat transfer medium flow rate, and possibly significantly higher flowimpedance.

Heat transfer efficiency is a function of the heat sink temperaturedistribution, heat transfer medium temperature and heat capacity, heatsink aerodynamic properties, heat sink surface heat transfer properties,and heat transfer medium flow properties, etc.

The optimization may employ one or more cost function, applied duringthe design phase for the heat sink system, and/or to supply theoperational parameters of the system in use. The heat sink is typicallyrequired to maintain the system within normal operational parameters,minimize temperature excursions (and associated thermal stresses), andto operate with minimum cost, e.g., fan operating power, andobjectionable noise. Static design optimization-phase cost functionparameters include size, cost, capacity, efficiency of operation, etc.

The present technology may provide a dual level fractal heat sink,having a spatial configuration with a fractal design, e.g., a multilevelbranching design, and a surface pattern with a fractal design, typicallyof a different type from the spatial configuration fractal design. Thesurface fractal may be, for example, a perforation pattern in a thinplate, or a texture on a smooth surface. Typically, the fractalgenerative algorithm for the configuration will be non-interactive orminimally interactive with the surface fractal generative algorithm,though at the overlap or interface between the regimes, some interactionor hybridization may occur.

Existing heat sinks typically achieve the primary objective ofmaintaining the cooled system within their operating range andmaintaining a sufficiently low thermal volatility. Therefore, theadvantages sought by the present technology are decreased acquisitioncost, operating cost, size, etc. Acquisition cost is a function ofmaterials cost and fabrication. While fabrication cost can vary based onmany factors, materials cost may be estimated based on commoditiesvalue, especially where the heat sink is typically formed of aluminum orcopper. Thus, for a homogeneous heat sink, the material and mass of theheat sink sets a lower bound on the acquisition cost. The operating costis typically set by the power consumed in causing the heat transfermedium to flow, e.g., a blower or fan for air flowing over the heatsink. Therefore, the heat sink according to the present technology mayprovide a design with lower mass and lower operating energy cost. Lowerenergy cost may be achieved by providing a lower thermal impedance(absolute) for equivalent thermal performance. Lower materials cost canbe achieved by providing a higher surface area or surface heat sheddingefficiency per unit mass. The present technology therefore provides anoptimized design for at least one of reduced fabrication cost and/ormaterial cost, and improved operating efficiency.

One advantage of a fractal or iterated function system-based solution tothis optimization is that it inherently avoids narrow band resonancebecause, both within the structure and for a heat transfer fluidinteracting with the structure, distances are not simple linear orgeometric integer multiples. Further, in a fractal branched architecture(if the structure is itself branched), the cross-section area tends toincrease with distance from the root, similar to an animal vascularsystem, thus increasing the efficiency as the system increases in size.

The second level fractal serves a different purpose from the firstlevel, and typically has a different scale range, fractal pattern, andpurpose. The second level modifies the surface texture to enhance heattransfer. The texture increases radiative and convective heat transfer.The fractal texture is efficient as it tends to reducesurface-to-surface radiative recapture, surface boundary layers, andacoustic emissions. If the scale range of the first and second levelsare generally non-overlapping, they may be separately optimized, and thegenerative algorithms may be independently defined. Alternately, theymay be coupled.

Optimization of the surface configuration of the heat sink may bedependent on temperature differential with respect to the coolingmedium; local cooling medium characteristics (heat capacity, density,temperature, viscosity); flow vector (direction, rate); radiativeabsorption and dissipation; noise/acoustic emission; fluid flowresistance; source/control over flow; change over time due to debris;and dynamic changes in heat load.

The optimization of the gross geometry of the heat sink is defined bymechanical constraints; convective and forced cooling fluid flowpatterns including intake and exhaust, and flow patterns; heat sinkmaterial characteristics; thermally induced changes in shape (may beintentional); branching and/or spatial morphology pattern, etc.

The entire structure has a maximum size on the order of centimeters ormeters, and a minimum controlled feature size of tens of microns or mm,therefore, the device has a scale range of at most ˜10⁴ (˜2¹³) (meterscale with 10 μm scale features) and a minimum ˜10¹ (2³) (cm scale withmm scale features). A fractal-type arrangement typically operates over arange of >2¹-2², and the fractal algorithm can be constrained tooptimize the entire scale range. However, such an algorithm may generatedesigns that cannot be manufactured in a cost-effective manner, orimpose strict requirements and tolerances for marginal gains. On theother hand, significant purposes of the fractal geometry may be achievedby employing fractal design principles over a subset of the scale range.Likewise, in many instances, the benefits may be achieved usingapproximately fractal designs, rather than requiring implementationstrictly according to a fractal formula. For example, it may be foundthat the effects of compliance with a fractal design formula overcertain scales are less important than uncontrolled air humidity ortemperature. If the uncontrolled variables dwarf the controlled ones,then it is likely that, over that range, strict compliance with theformula is non-essential. Note that, if the structure deviates from thegenerating formula over a scale range, that any smaller scale rangeshould be optimized based on the actual configuration, and not thetheoretical one.

The resulting structure therefore has many different factors whichinfluence optimization, some of which overlap. Indeed, there is no limitof two levels of optimization, and rather there may be multiple levels.Because each level requires a scale range (e.g., 2¹ to 2⁴), and thetransition between scales should be discrete (in order to define twoseparate optimizations rather than a single continuum), it is seen thata typical system would be limited to 2-4 levels of size ranges. Forexample, in a medium scale, between the gross morphology and averageheat distribution over space, and the surface texture and aerodynamiceffects for convective heat transfer, a middle scale may be providedwhich optimizes convective channeling of the heat transfer fluidproximate to the heat sink structure. As discussed above, each level maybe asymmetric, symmetric, or arbitrary (e.g., human heuristic), and mayhave an optimized transition between levels, a smoothed transition or anabrupt transition.

The surface texture (small scale features) may be mapped onto themorphology (large scale features), and as such, only at the terminalbranches of the heat sink do the scales of a dual scale heat sinkoverlap, in which case the mapping algorithm for applying the texturecan account for the termini (without requiring interactive modificationof the morphology). In the case of a >2 scale level design, each scaletransition can be blended or fit. Typically, in the transition region,the changeover will be defined more by functionally defined prohibitionsthan by blending rules. For example, a transition zone that createsunnecessary turbulence in air flow without contributing materially toheat transfer would be disallowed, while a piecewise fit approximationthat does not cause large heat transfer efficiency discontinuities wouldbe permitted, even if not formally optimized according to an algorithm.

Typically, a design in accordance with the present technology willdisplay a change in pattern within at least one particular scale range,as opposed to a uniform pattern mapped on a lower scale structure. Ofcourse, in an embodiment with two or more scale ranges, only a singlesuch scale range should represent a fractal (affine or self-similar, oriterated function system) design, and the others may be defined bydifferent paradigms. Indeed, according to one embodiment,characteristics of one or more scale range is predefined, and aself-optimizing algorithm with fractal characteristics is run tooptimize the further design with the predetermined scale rangecharacteristics as a limit or constraint. Thus, for example, a surfacetexture, which may be defined by a manufacturing process, may beselected as the highest scale feature. Underlying this texture is anarrangement of surfaces and the radiative and convective heat transferto the surfaces, while at the lowest level is the mechanical constraintsof the heat source, heat transfer fluid flow patterns, fan (if any),intake, exhaust, adjacent structures, etc. In this case, the lowestlevel and the highest level both have significant constraints which arenot controlled by any fractal algorithm, and therefore the purpose ofthe algorithm is to optimize the heat transfer and efficiency issuesbetween the constraints.

According to another example, a textured surface coating is applied to abase structure with a smooth surface, wherein the texturing is mildlydependent on the shape of the underlying surface. In this case, thealgorithm that defines the smooth surface configuration is alsodependent on the characteristics of the surface coating and itsapplication technology. However, by controlling the underlying surfacemorphology, the surface texture is also modified, resulting in spatialvariations in texture in addition to the spatial variations insymmetry/shape. An example of such a surface texture material is wrinkle(crinkle) paint, whose resulting texture is dependent on coatingthickness underlayer, drying, etc. For example, a wrinkle paint may beformed of a high thermal transfer material, such as copper powder. Thecoating need not be formed over the entire heat sink, and thus it may beselectively applied to regions where the higher surface area and flowdisruption are beneficial. Typically, the wrinkle paint would result ina high flow impedance, and therefore is preferred to be applied on lowsurface velocity or “hot” portions of the device, where the high surfacearea and/or turbulent flow may be beneficial in spite of the lower flowefficiency. On the other hand, in regions with lower thermaldifferentials, a smooth surface may be preferred. Indeed, the algorithmfor defining the morphology of the heat sink may be dependent on theresulting characteristics of deposition process of a coating on the heatsink; that is, the shape of the heat sink may be optimized for thedeposition process for the coating, to intentionally apply an unevencoating thickness.

In a design according to the present technology, the small andlarge-scale features may be overlapping or non-overlapping. That is, insome cases, there is a gap between the smallest scale features addressedby the large-scale feature definitions, and the largest featureaddressed by the small-scale feature definitions, in which case thesemay be non-interactive or weakly interactive, and may be definedseparately or purely sequentially. On the other hand, where the scalesoverlap or are nearly contiguous, it may be desirable to optimize bothscales to avoid a discontinuity at the boundary, which may require adual optimization.

The heat sink may be designed to work in conjunction with a variable fanstructure, which may vary in speed/air volume, impingement direction(s),etc. Further, because the heat dissipation efficiency is a function oftemperature differential, the design may have an oscillating fan thatexposes different portions of the heat sink to air flows over time, withthe result that temperatures in various portions of the heat sink alsooscillate. While such a design will optimally be larger than a staticheat sink, it may also display higher energy efficiency at low loads,while having a higher peak dissipation capacity.

The fluid flow process, especially under dynamically changingconditions, can be complex. For example, the flow can cause turbulentflow around the heat exchange elements, which induce complex pressuredifferentials, vibrations, and inertial flow patterns. Dynamicallychanging the flow rate or flow pattern can help distribute the turbulentdynamics over various regions of the heat sink surface. Thus, the entiresurface of the heat sink need not be subject to continual high fluidflow rates, and only a small portion of the surface at any given timemight be subject to a “jet” of fluid flow, thus reducing the energydisadvantage. The jet may be strategically focused on portions of theheat sink. When the jet (or more generally, high flow rate stream) isfocused or directed at the hot portion of the heat sink, higherconvective heat transfer will occur. However, discontinuous high flowrates may be advantageous, since a reduced fluid flow on a region willtend to cause a diffusive heat transfer to the heat transfer materialunderlying the cooled surface, and thus lead to higher efficiency heattransfer when the jet or stream returns. Meanwhile, the jet or streamcan be directed to other portions of the heat sink. This, in turn,causes dynamic temperature gradients within the heat sink, which can becontrolled to cause pulsatile heating at the periphery of the heat sink,especially in a branched network. Thus, for example, in a fractalbranched heat sink, the stream of fluid can be controlled to permitvarious regions of the heat sink to undergo heating and cooling cycles,such that the hot spots on the heat sink are dynamically controlled tobe selectively cooled.

A model of the process may be employed as part of the design of the heatsink or thermal transfer structure, or as a part of a control system forits operation. Available control parameters include heat transfer mediumcharacteristics (e.g., in air, density, humidity, liquid [water]droplets, etc.), bulk flow rate, bulk flow vector, inhomogeneous flowcharacteristics (e.g., jets, asymmetries, spiral flows, vibrations andresonances, turbulence, etc.), structural configuration (e.g., spacingsand angles, aperture patency, etc.), internal heat flow control (e.g.,microchannels, heat pipes, continuity of heat flow paths, etc.),radiative characteristics, surface roughness, etc.

The control system, which e.g., controls a fan speed or other or morecomplex system, may be dependent on sensors, such as thermal sensors(thermistors, thermocouples, bipolar junctions, etc.), thermal cameras,passive infrared sensors, optical cameras reading thermally responsivecoatings on the heat sink, or the like, may be used to monitor internaland/or surface temperatures of the heat sink, and adaptively supplycoolant as appropriate. Sensors may also be used to detect surfacecontamination of the heat sink, and a need for removal of thecontamination, which may be by the fluid jet, vibrational excitation, orother means. The heat sink design may, in turn, be optimized for thelimited degrees of freedom available to a dynamically adjustable fluidflow control system, for example exposing small area hotter portions ofthe heat sink to high-flow cooler heat transfer medium, while exposinglarge area cooler portions of the heat sink surface to lower flow rate,potentially warmer medium (but, below the surface temperature).Likewise, in cases where the heat transfer medium is heated past theequilibrium point of the nearby heat sink structures, it should be shedfrom the heat sink, while heat transfer medium cooler than theequilibrium point of the nearby structures should be directed to thosestructures to provide additional cooling, where the flow does not reduceefficiency. This may be altered dynamically, by providing flow dampersto control exhaust paths of the heat transfer fluid through the heatsink structure, which will typically be an asymmetric 3D structure,which will typically include fluid flow channels or spaces.

The fluid flow over the heat sink surface can also cause acousticresonance, which in the case of a heat sink having a fractal geometry,can be, in the aggregate, a broadband resonance. In many cases, acousticemissions from a heat sink system are undesirable, and should beminimized. However, in some cases, certain acoustic emissions areacceptable, and may be specifically exploited to cause a thinning ordisruption of the surface boundary layer of heart transfer medium, thusincreasing heat transfer efficiency. When an acoustic resonance occurs,this increases the bulk flow of heat transfer medium particles, and assuch may increase mixing at the interface. Turbulence near the interfacewill typically directly disrupt the boundary layer. In each case, thismay be exploited to improve the heat transfer efficiency. It is notedthat, in a contained system, a number of options are available to reducenet acoustic emissions, even when internal sounds are generated.According to one option, acoustic filters are employed, which aretypically passive. According to another option, active noisecancellation is employed, in which the phase and amplitude of acousticvibrations at a location, which is typically constructed to be a portrepresenting a node having homogeneous acoustic properties, is predictedbased on an acoustic sensor, e.g., a microphone. An actuator is thendriven which seeks to reduce the net acoustic emissions at the port.Advantageously, this actuator is configured to increase or reinforceinterface acoustic effects, so that the active noise cancellation itselfserves to increase heat transfer by reducing or disrupting the surfaceboundary layer of the heat transfer medium.

The heat transfer medium flow can be controlled or provided in apulsatile or oscillating manner, causing inertial transfer of energy tomedium or debris on the surface, resulting in separation from theunderlying heat exchange surface. The flow can also cause stress andstrain on debris coating on the surface, causing separation along thesurface plane. The time varying flow can effectively remove theaccumulated surface debris. A static flow in some cases could alsoreduce accumulation, but it is noted that the static flow is presumed tobe associated with the accumulation conditions, and maintenance ofsufficient continuous flow conditions to remove accumulation may consumeexcess energy, noise, and abrasion of the heat exchange surfaces.

Confined liquid heat sinks limit flow of cooling liquid within a tube orchannel. (Unconfined liquids may be sprayed over an open heat transfersurface). The cross-section area of the channels, and fluid flow rate,is relatively constant in the aggregate as the fluid travels through thebranched channels. However, when one considers the logistics of atypical design, the flow channels are either planar or the design isradially symmetric.

In a planar configuration, a base of the heat sink interfaces with theheat source, and the fluid flows through the structure above the heatsource to withdraw heat.

See, Escher, W., B. Michel, and D. Poulikakos “Efficiency of optimizedbifurcating tree-like and parallel microchannel networks in the coolingof electronics.” International Journal of Heat and Mass Transfer 52.5(2009): 1421-1430;

Wang et al., “Flow and Thermal Characteristics of Offset BranchingNetwork,” 12 Aug. 2009, International Journal of Thermal Science, Vol.49, Pages 272-280;

Yongping, Chen, et al. “Characteristics of Heat and Fluid Flow inFractal Tree-like Channel Heat Sink [J].” Acta Aeronautica EtAstronautica Sinica 3 (2010): 008;

Xu, Peng, et al. “Thermal characteristics of tree-shaped microchannelnets with/without loops.” International Journal of Thermal Sciences48.11 (2009): 2139-2147;

Ghodoossi, L., “Thermal and hydrodynamic analysis of a fractalmicrochannel network”, Energy Conversion and Management 46 (2005)771-788;

Liu, Shutian, Yongcun Zhang, and Peng Liu. “Heat transfer and pressuredrop in fractal microchannel heat sink for cooling of electronic chips.”Heat and Mass Transfer 44.2 (2007): 221-227;

Alharbi, Ali Y., Deborah V. Pence, and Rebecca N. Cullion. “Thermalcharacteristics of microscale fractal-like branching channels.” Journalof Heat Transfer 126.5 (2004): 744-752;

Salakij, S., et al., “Modeling in situ vapor extraction duringconvective boiling in fractal-like branching microchannel networks”,International Journal of Heat and Mass Transfer 60 (2013) 700-712;

Apreotesi, Mario A., “Microscale Thermal Management Utilizing VaporExtraction from a Fractal-like Branching Heat Sink”, M.S. Thesis,University of Oregon (2007),

Hong, F. J., et al. “Conjugate heat transfer in fractal-shapedmicrochannel network heat sink for integrated microelectronic coolingapplication.” International Journal of Heat and Mass Transfer 50.25(2007): 4986-4998;

Lee, Yong-Jiun, Poh-Seng Lee, and Siaw-Kiang Chou. “Enhancedmicrochannel heat sinks using oblique fins.” ASME 2009 InterPACKConference collocated with the ASME 2009 Summer Heat Transfer Conferenceand the ASME 20093rd International Conference on Energy Sustainability,American Society of Mechanical Engineers, 2009;

Senn, S. M., and D. Poulikakos “Laminar mixing, heat transfer andpressure drop in tree-like microchannel nets and their application forthermal management in polymer electrolyte fuel cells.” Journal of PowerSources 130.1 (2004): 178-191;

Xiangqi, Wang. “New approaches to micro-electronic component cooling.”PhD diss., 2007 (National University of Singapore);

U.S. Pat. No. 6,688,381; US 2008037927; U.S. Pat. Nos. 6,333,852;7,256,751.

The temperature gradient within the heat sink having a planar flow planewould generally be decreasing with distance away from the interface,with the bulk material in and near the fluid flow plane largelyisothermal.

The present technology may be applied to both external surface heatdissipation devices, and/or to confined heat transfer fluid heat sinks.

In a radially symmetric arrangement, typically a constant cross sectionbranched solid heat sink (e.g., extruded), see e.g., U.S. Pat. No.4,715,438; US 20080080137, US 20090050293; U.S. Pat. Nos. 8,295,046;2,535,721, may be placed within a shell or confinement, and a containedfluid permitted to contact the exposed surfaces. In this case, the fluidpath is not highly constrained, and the operating temperature may beunstable, for example due to nearly adiabatic movement of fluid massesas a result of density and viscosity differences of the heated fluid. Anextruded heat sink is generally a suboptimal shape, since the moredistal portions of the structure a constant higher surface by lowerthermal gradient. Indeed, due to possible adiabatic movement of hotfluid, in some cases the fluid can heat portions of the heat sink. A“structurally complex” heat sink is provided in US 20090321045, butwithout branching networks and without optimized regional heterogeneity.In a closed, vacuum or filtered system, typically no accumulation ofdust, debris or precipitate on the heat exchanger surface occurs.

Most heat sinks are designed using a linear or exponential relationshipof the heat transfer and dissipating elements. According to the presenttechnology, fractal geometry paradigms are employed, which are thosewhich have self-similar characteristics over a range of scales. Thisself-similarity may be symmetric or asymmetric, and may involvebranching or subdivision. Some fractals are random fractals, which arealso termed chaotic or Brownian fractals and include random noisecomponents. In deterministic fractal geometry, a self-similar structureresults from the repetition of a design or motif (or “generator”) usinga recursive algorithm, on a series of different size scales. As aresult, certain types of fractal images or structures appear to haveself-similarity over a broad range of scales. In a symmetric design, theself-similar features may be identical and have well-defined scales,while in an asymmetric design, no two ranges within the design areidentical or purely scaled. As discussed above, the heat sink accordingto the present technology need not be a pure fractal, and thus mayviolate a generative function, and yet still operate according to thedesign principles.

One definition of a fractal is “a rough or fragmented geometric shapethat can be split into parts, each of which is (at least approximately)a reduced-size copy of the whole.” Mandelbrot, B. B. (1982). A recursivealgorithm may describe the structure, causing self-similarity. See, TheFractal Geometry of Nature. W.H. Freeman and Company. ISBN0-7167-1186-9; en.wikipedia.org/wiki/Fractal. In practicalimplementations, the scale of the smallest features, which remain trueto the generating algorithm, may be 3-25 iterations of the algorithm. An“approximately” fractal structure is one that has various deviationsfrom theoretical, such as a limited number of iterations of thegenerative algorithm, perturbations and artifacts of implementation, orintentional bias.

Fractal theory is related to chaos theory. See,en.wikipedia.org/wiki/Chaos_theory.

See also, Sui, Y., Teo, C. J., Lee, P. S., Chew, Y. T., & Shu, C.(2010). Fluid flow and heat transfer in wavy microchannels.International Journal of Heat and Mass Transfer, 53(13), 2760-2772;

Garibaldi, Dott Ing Pietro. Single-phase natural circulation loops:effects of geometry and heat sink temperature on dynamic behavior andstability. Diss. Ph. D. Thesis, 2008;

Fichera, A., and A. Pagano. “Modelling and control of rectangularnatural circulation loops.” International journal of heat and masstransfer 46.13 (2003): 2425-2444;

Fichera, Alberto, et al. “A modeling strategy for rectangular thermalconvection loops.” World Congress. Vol. 15. No. 1. 2002;

Crane, Jackson T. Radial parallel plate flow with mechanical agitation.Diss. Massachusetts Institute of Technology, 2013.

This fractal nature is useful in a heat sink because the rate at whichheat is transferred from a surface, either through convection or throughradiation, is typically related to, and increasing with, the surfacearea. Of course, due to limitations in the technology used to buildthese heat sinks, engineering compromise is expected. However, a featureof an embodiment of the designs proposed herein is that vortices inducedby fluid flow over a heat transfer surface will be chaoticallydistributed over various elements of the surface, thus disrupting thestagnant surface boundary layer and increasing the effective surfacearea available for heat transfer, while avoiding acoustic resonancewhich may be apparent from a regular array of structures which producevortices and turbulence.

Further, a large physical surface area to volume ratio, which isgenerally useful in heat sink design, can still be obtained using thefractal model. In addition, fractal structures provide a plurality ofconcave regions or cavities, providing pockets of separated flow whichcan generate self-sustaining oscillations and acoustic resonance. Thesepockets serve to reduce the acoustic resonance in turbulent flowingfluid (as compared to flat or Euclidian surfaces), thus allowing formore effective heat transfer between the fractal structure and thesurrounding fluid, thereby making the fractal structure ideal for a heatsink.

U.S. Pat. No. 7,256,751 (Cohen), discusses fractal antennas. In thebackground of this patent, Cohen discusses Kraus' research, noting thatEuclidian antennas with low area (and therefore low perimeter) exhibitvery low radiation resistance and are thus inefficient. Cohen notes thatthe advantages of fractal antennas, over traditional antennas withEuclidian geometries, is that they can maintain the small area, whilehaving a larger perimeter, allowing for a higher radiation resistance.Also, Cohen's fractal antenna features non-harmonic resonancefrequencies, good bandwidth, high efficiency, and an acceptable standingwave ratio.

In the instant technology, this same wave theory may be applied tofractal heat sinks, especially with respect to the interaction of theheat transfer fluid with the heat sink. Thus, while the heat conductionwithin a solid heat sink is typically not modeled as a wave (thoughmodern thought applies phonon phenomena to graphene heat transport), thefluid surrounding the heating certainly is subject to wave phenomena,complex impedances, and indeed the chaotic nature of fluid eddies mayinteract with the chaotic surface configuration of the heat sink.

The efficiency of capturing electric waves in a fractal antenna,achieved by Cohen, in some cases can be translated into an efficiencytransferring heat out of an object to be cooled in a fractal heat sinkas described herein. See, Boris Yakobson, “Acoustic waves may coolmicroelectronics”, Nano Letters, ACS (2010). Some physics scholars havesuggested that heat can be modeled as a set of phonons. Convection andthermal radiation can therefore be modeled as the movement of phonons. Aphonon is a quasiparticle characterized by the quantization of the modesof lattice vibration of solid crystal structures. Any vibration by asingle phonon is in the normal mode of classical mechanics, meaning thatthe lattice oscillates in the same frequency. Any other arbitrarylattice vibration can be considered a superposition of these elementaryvibrations. Under the phonon model, heat travels in waves, with awavelength on the order of 1 μm. In most materials, the phonons areincoherent, and, therefore, on macroscopic scales, the wave nature ofheat transport is not apparent or exploitable.

The thermodynamic properties of a solid are directly related to itsphonon structure. The entire set of all possible phonons combine in whatis known as the phonon density of states which determines the heatcapacity of a crystal. At absolute zero temperature (0° K or −273° C.),a crystal lattice lies in its ground state, and contains no phonons. Alattice at a non-zero temperature has an energy that is not constant,but fluctuates randomly about some mean value. These energy fluctuationsare caused by random lattice vibrations, which can be viewed as agas-like structure of phonons or thermal phonons. However, unlike theatoms which make up an ordinary gas, thermal phonons can be created anddestroyed by random energy fluctuations. In the language of statisticalmechanics this means that the chemical potential for adding a phonon iszero. For a more detailed description of phonon theory, see theWikipedia article thereon available at en.wikipedia.org/wiki/Phonon.

In certain materials, such as graphene, phonon transport phenomena areapparent at macroscopic levels, which make phonon impedance measurableand useful. Thus, if a graphene sheet were formed to resonate at aparticular phonon wavelength, the resonant energy would not be emitted.On the other hand, if the graphene sheet were configured using a fractalgeometry, the phonon impedance would be well controlled over a broadrange of wavelengths, with sharp resonances at none, leading to anefficient energy dissipation device.

One aspect of the technology therefore employs a thermally responsivetechnology, such as a memory metal actuator (which may be passive oractive), or other active or passive element, to change the configurationof the heat sink under various conditions. It is noted that in anautomotive radiator, a thermostat is provided to shunt flow around theradiator when the engine is cool. This is distinguished herein, invarious alternate ways. For example, a variable geometry heat sinkaccording to the present technology may have an external surface exposedto an unconstrained heat transfer medium, such as air.

See, Baurle, R. A., and D. R. Eklund. “Analysis of dual-mode hydrocarbonscramjet operation at Mach 4-6.5.” Journal of Propulsion and Power 18.5(2002): 990-1002;

Cockrell Jr, Charles E. “Technology Roadrnap for Dual-Mode ScramjetPropulsion to Support Space-Access Vision Vehicle Development.” (2002);

Boudreau, Albert H. “Hypersonic air-breathing propulsion efforts in theair force research laboratory.” AIAA 3255.1 (2005): 10;

Kay, Ira W., W. T. Peschke, and R. N. Guile. “Hydrocarbon-fueledscramjet combustor investigation.” Journal of Propulsion and Power 8.2(1992): 507-512;

Jackson, K., et al. “Calibration of a newly developed direct-connecthigh-enthalpy supersonic combustion research facility.” AIAA paper(1998): 98-1510;

Donbar, J., et al. “Post-test analysis of flush-wall fuel injectionexperiments in a scramjet”, AIAA Paper 3197 (2001): 2001;

Gruber, Mark, et al. “Newly developed direct-connect high-enthalpysupersonic combustion research facility.” Journal of Propulsion andPower 17.6 (2001): 1296-1304;

Andrews, Earl H. “Scramjet development and testing in the UnitedStates”, AIAA paper 1927 (2001): 2001;

Palac, Donald T., Charles J. Trefny, and Joseph M. Roche, PerformanceEvaluation of the NASA GTX RBCC Flowpath, NASA, Glenn Research Center,2001;

U.S. or foreign Patent and Published Patent Application Nos.2003/0155110; 2004/0187861; 2005/0245659; 2009/0016019; 2009/0321047;2010/0089549; 2010/0236236, 2010/0252648; 2011/0174462; 2012/0293952;2014/0360699; 4,654,092; 4,931,626; 5,371,753; 5,483,098; 5,548,481;5,510,598; 6,128,188; 6,330,157; 6,689,486; 7,080,989; 7,778,029;8,228,671; 8,385,066; JP 03-070162; JP 04-291750; JP 61-098565; JP63-006915; WO 99/04429.

For example, a thermodynamic model of the system, encompassing at leastthe heat source, the heat sink, the thermal transfer medium, and adevice to induce thermal transfer medium flow, may determine, under eachset of conditions, the optimal configuration. For example, at low loads,the heat sink may operate passively, without flows induced by an activedevice to induce flow in the thermal transfer medium. In such a case,radiative heat transfer may be important, as well as thermally-inducedconvection. Under high loads, the active device to induce flow in thethermal transfer medium may induce maximum flows, and the heat sinkconfigured for minimal turbulence with laminar flows where possible. Inintermediate states, the system may assume a configuration which isoptimized according to a cost function, which may involve the effect ofheat/temperature on the heat source, energy consumed by the activedevice to induce flow in the thermal transfer medium, noise resultingfrom induced flow, etc. This allows efficient use of an “oversized” heatsink, since the heat sink characteristics are variably controlled. Inthese intermediate states of configuration, efficiency may be improvedby allowing the heat sink to assume a variable configuration. Since theoptimum heat sink configuration depends on, e.g., ambient temperature,humidity, atmospheric pressure, heat load, air flow rate, gravitationalvector with respect to the heat sink, etc., the model should explore therange of combinations of the device to induce thermal transfer mediumflow, the variable geometry, and to a lesser extent, control over theheat source. An example of the later is that for a given powerdissipation, it may be more efficient to have thermal cycles reaching amaximum temperature than a constant temperature. During the cycles, thegeometry may change. Indeed, if the system is not in a static steadystate, the geometry may optimally change during or in anticipation oftemperature changes. An example here is that as the heat source producesa heat peak, the heat diffuses over time through a solid heat sinkmaterial. There is a lag, and so the temperature of the heat source isdifferent that the temperature of the heat sink, and the heat sinkitself has variations in temperature at different positions. Typically,there is a single actuator which controls the entire heat sink, thoughthis is not a limitation, and there may be multiple actuators to controldifferent parts of the heat sink independently or semi-independently.The device to induce thermal transfer medium flow may have a variableflow rate, and also may have multiple independently controlled portions.However, as the heat begins to peak, the device to induce thermaltransfer medium flow may also increase activity. This, in turn, canreduce the temperature of various portions of the heat sink, dependingon the relationship of the device to induce thermal transfer medium flowand the variable geometry heat sink. Thus, the entire system may operatein a phased cyclic or dynamic manner, with asynchronous maxima andminima of the various functions.

In practice, a heat sink may be provided for a microprocessor havingmultiple cores. Under low load, the device to induce thermal transfermedium flow may be off, or at a low flow rate. The heat sink in thiscase optimally has the greatest spread for radiative and passiveconvective cooling. In case of a higher load, the processor itself mayhave the option of distributing the load over multiple cores, andspatially spreading the heat dissipation, or concentrating the load in asingle core which may get hot. Since temperature differentials increaseheat flow, the concentrated heat source may selectively transfer heat tosub-portion of the heat sink, and thus that portion may be able toefficiently shed the heat under the passive or low energy cost state.

As the load further increases, the processor as a whole typicallybecomes thermally limited, and as a result, the entire die or processorcomplex is treated as a unitary source, spreading heat to all elementsof the heat sink. Initially, the temperature is low, and the systemwould seek to operate in the most efficient state of the device toinduce thermal transfer medium flow. This may include laminar flow overthe heat dissipating elements of the heat sink.

In the next regime, the heat increases, and as a result, the device toinduce thermal transfer medium flow must increase its flow rate. At thispoint, a compromise may be made, between minimum energy cost (and thus aminimization of the energy to drive the device to induce thermaltransfer medium flow), and effective heat dissipation. In this regime,the heat sink may be configured to induce turbulence in the medium flowaround it. This, in turn, increases the resistance to flow, but reducesthe boundary layer effect. Advantageously, in this regime, a fractalphysical relationship of element of the heat sink may act to reduce peakacoustic emission with respect to frequency. Likewise, by avoiding sharpacoustic resonances, there may be a more effective transfer of heat withlower losses as acoustic energy. Further, the interaction of theelements of the heat sink may be further optimized to achieve higherefficiency.

Finally, at maximum heat load, presumably at the limit of the heat sink,the system enters a maximum heat dissipation mode. For example, thismode is one traditionally analyzed as the maximum capacity of the heatsink and device to induce thermal transfer medium flow system, and assuch would typically assume or nearly assume a traditional optimizedgeometry. However, both due to the fact that the system may includefractal geometry elements for other regimes of operation, and becausethese may be exploited to gain efficiencies over traditional symmetricand regular geometries, the maximum heart dissipation configuration maybe somewhat different than a parallel plate heat sink, for example.

Not all regions of the heat sink need to operate within the same regimeat the same time, and even under a steady state heat load, may varycyclically, randomly or chaotically (over a relevant timescale). Theterm “chaotically” is intended to assume its technical meaning underchaos and fractal theory, and not adopt a lay interpretation. On theother hand, “randomly” is intended to encompass true randomness,pseudorandom variations, and deterministic changes that over therelevant timescale have statistical characteristics that modelrandomness within an acceptable margin of error, the acceptabilityrelating to achieving a suitable regime of operation. For example,because some attributes of turbulent flow are random, even though theyare more technically chaotic, the random features may be used toadvantage. For example, the device to induce thermal transfer mediumflow may be subject to a tinsel type flow disruptor, which in someregimes appears to be a random variation in air flow speed, direction,vortex, etc. While this may increase noise, it also can createpersistent disruptions in boundary layers, over time, even on smooth andregular heat sink elements. That is, the heat sink geometry and/or thedevice to induce thermal transfer medium flow, may have fractal orchaotic tendencies.

The geometry may involve branching elements, to increase surface area ofthe elements. An actuator may be used to alter angles or even to openand close branches. For example, a heat sink formed of a shape memoryalloy (SMA) (such as Nitinol), may be produced by an additivemanufacturing process, e.g., a 3D printer or 2.5D printer. Such a devicemay be thermally processed to have characteristic shape changes attemperature transitions, and indeed, the composition of the alloy may becontrolled during fabrication to produce a variety of transitiontemperatures. Therefore, a 3D heat sink may be provided which inherentlychanges shape through a series of transitions as the temperature isincreased and decreased. In this embodiment, the changes tend to bemonotonic with increasing temperature, though by engineering the anglesand physical configuration, the actual physical shape and heatdissipation properties may assume a non-monotonic function. Note that inthis embodiment, it is generally preferred that only the branch pointsare formed of SMA, and the bulk be formed of a high thermal conductivitymaterial, such as copper and/or silver, or to a lesser extent, aluminum.The dynamic operation may be applied to the lower-level fractalarrangement, while the second level may remain static.

Actuators, which may be SMA, solenoids, bimetal, magnetic, or otherwise,may be provided and controlled to change the position of repositionableelements. Control can be exercised which independent of temperature.Typically, the number of controlled elements is constrained due tomanufacturing and control feasibility issues. The actuators may alter aspacing, angle, position, or engagement of heat sink elements, or airflow impinging on the elements. When a set of regularly spaced and sizedelements are controlled according to a constant or spectrally-defineddistribution, this can be controlled to operate within highlypredictable regimes. On the other hand, if the elements are notregularly sized and spaced, or are controlled in irregular manner, theresulting fluid dynamics will likely require a statistical flow (e.g.,Monte Carlo) analysis, rather than permitting simplifying staticfunction/linear response presumptions. This is will especially be thecase if the thermal time-constants of the heat flow from the heatsource, to the heat sink, and then to the heat transfer fluid, are nearor within the range of time-constants of the turbulence or chaoticallyvarying flows of the heat transfer fluid. Typically, the thermal heattransfer time-constants are longer than the turbulent or chaoticvariation time-constants, and therefore meeting this presumptionrequires either generating low frequency turbulent or chaotic variationsof the heat transfer fluid medium, or making the heat sink (and perhapsother elements) with short time-constants, such as usingshort/thin/small elements, using phonon transport phenomena, or othermeans.

Controlled shape or morphology of the heat sink typically operates atthe largest size scales of the heat sink. However, it is also possibleto control surface configuration (e.g., texture) at a small scale, suchas using holes to facilitate heat exchange, or bimetallic elements thatbend or snap at predefined temperatures, deployable cylinders, or othersmall-scale features that typically alter aerodynamic properties of asurface. For example, it may be desirable for terminal branches of ahierarchical branched heat sink to have a turbulence, which increaseswith temperature. In that case, a cool heat sink surface is smooth, andoffers low resistance to heat transfer fluid flow, low noise, but loweffect on heat dissipation. At high temperatures, one wishes to ensureintimate contact of the relatively cooler heat transfer fluid with theheat sink, which can be increased by disrupting the laminar flowpatterns, for example by having surface features that protrude into thefluid stream. While this increases noise and resistance to fluid, italso offers higher heat transfer capability, especially if the pressureinducing flow of the heat transfer fluid is increased.

An adaptively controlled system may be implemented, which may powerdissipation, thermal, air flow, acoustic, and other sensors to control aconfiguration of the heat sink itself, or air flow surrounding the heatsink. For example, a FLIR One Gen 3 imager (FLIR Systems, WilsonvilleOreg.) may be used to monitor heat sink temperatures. As the temperatureof a region of the heat sink rises, adaptive steps are taken toselectively cool that region, without substantially heating otherregions in a manner that would reduce net heat transfer. In some cases,the heat sink is regioselective, and therefore the adaptivity must alsoaddress where the hot spot is, and how best to cool that spot. Inaddition, cool spots of the heat sink may be addressed by reducing airflow or other effects, to better use the full volume of the heat sink,under the full range of conditions. In other cases, the IR imager is tooexpensive. In that case, for example, an optic imager and liquid crystaltemperature indicators may be employed. Alternately, thermal sensors,such as thermistors, bipolar junctions, thermocouples, bimetalindicators, or the like may be used to assess local or regionaltemperature conditions. These sensors may be selectively located atnodes of the design. While selective air jet impingement is one optionfor controlled cooling of the heat sink, more typically the cost andenergy cost of the air supply is a factor, and therefore the designincludes a fan or centrifugal blower, whose sole control is fan speed.However, in conjunction with the heat sink, and especially afractal-shaped heat sink, the air flow will induce flow perturbationsaround the heat sink elements, which will be detectable as vibrations,i.e., sounds, resulting from turbulence or resonance. An array ofmicrophones can assist in locating the source of the sounds. In thetypical design, the heat sink combined with the heat source has areproducible het distribution pattern, though this may change over timedue to particulate or grease accumulation, ambient temperature,humidity, illumination (radiation load), and other effects. Therefore,the fan speed may be controlled not only dependent on the temperature ofthe device to be cooled, but also on the power required to operate thefan (which may follow a non-linear and/or non-monotonic function due tothe aerodynamic effects), and a control signal dependent on acousticemissions. For example, in some modes of operation, it may be desirableto suppress acoustic emissions, even at risk of less efficientoperation. Therefore, when the acoustic emissions are detected, the fanspeed is changed (typically increased, by potentially decreased ifwithin the margin of safety), to reduce the undesirable acousticemissions. In other modes of operation, maximization of heat transferefficacy is preferred, and the fan operated at speeds which createturbulence around hot elements of the heat sink, and thus increase heattransfer at those locations by reducing the surface boundary layer.Because the typical response is repeatable, a lookup table or algorithm,or other predictive model, employed to determine, in a given operatingstate (e.g., power dissipation, environmental conditions, etc.), whatthe temperature profile of the heat sink elements will be. Then, a fanspeed is determined that will best achieve the objective. This objectiveis, for example, acoustically responsive, to control the acousticemissions. Acoustic feedback is useful because at a given time, theexact acoustic response may be non-deterministic due to fouling ofsurfaces, air flow imperfections, etc. In some cases, the system maytake advantage of acoustic masking, and thus produce non-objectionablenoise under the circumstances. See, U.S. Pat. No. 7,974,714. It is notedthat vibrational air movement may also be induced by vibrating the heatsink. This may be induced by displacing the heat sink as a whole, orvibrating portions of the heat sink, such as with an electromagneticdevice or piezoelectric device.

The time-constant(s) of the thermal transfer medium flow may be muchshorter than the relevant thermal time-constants of the heat source andheat sink, and the purpose of the turbulent or chaotic disruption is toalter the convective heat transfer characteristics of the heat sink,such as reducing the boundary layers or making them dynamically changingover time and space.

Another aspect of the technology involves planar heat sinks, such asused in antenna designs. In this case, the present technology may havecorresponding effect to that discussed above, especially where a deviceto induce thermal transfer medium flow is provided to cool a generallyplanar heat sink system. It is noted that any heat sink in actualitymust be considered in three dimensions, and the fact that it may haveexpanses of a thin uniform thickness layer does not defeat use ofthree-dimensional analysis to understand its functioning andoptimization. In the case of a printed circuit board-type heat sink, avariable geometry or printed traces on a rigid circuit board istypically infeasible. On the other hand, if the circuit board is notrigid, or the traces not simply copper sheet intimately adhered to thesubstrate, it may be feasible to apply dynamically varying designprinciples to profited-type circuit boards.

Similarly, where a planar heat sink structure serves a secondarypurpose, such as an antenna, the physical configuration may beconstrained by this other purpose. However, the device to induce thermaltransfer medium flow is typically not so constrained, and thereforeprovides a controllable variable. Further, in many cases, therequirement for “thinness” of a 2D heat sink does not preclude texturingor perforation on an exposed surface, which itself may have a fractalgeometry on a small scale.

In some cases, a variable geometry may be achieved by altering flowcharacteristics of thermal transfer medium flow and, for example, adeflector may be controlled to change a direction of impingement.Advantageously, a surface of a heat sink can have anisotropic features,which respond differently to different flow direction. Thus, theefficiency of the fan can be optimized other than by fan speed alone, toprovide another control variable. This may have particular importancewhere the fan itself is highly constrained, and cannot simply be madeoversized, or where energy efficiency is an overriding concern.

The technology is not limited to a cooling gas, and may encompassliquids. Typically, cooling liquids are recycled, and therefore operatewithin a physically closed system. Use of a fractal branching fluidnetworks is known, but various principles discussed above, such asvariable geometry, variations in flow rate over different regimes ofoperation, different directions of flow over surfaces, and intentionalinduction of chaotic flow patterns may be adopted.

Many fractal designs are characterized by concave regions or cavities.See, for example, FIGS. 2 and 3 . While sets of concavities may beuseful in improving aerodynamics and fluid dynamics to increaseturbulence, if they are disposed in a regular array, they will likelyproduce an acoustic resonance, and may have peaks in a fluid impedancefunction. On the other hand, the multiscale nature of a fractalgeometric design will allow the system to benefit from the concavities,while avoiding a narrowly tuned system.

Benefits of a fractal heat sink for the purpose of dissipating heat,over a traditional heat sink having a Euclidian geometry may include:(1) the fractal heat sink has a greater surface area, allowing for moreexposure of the hot device to the surrounding air or liquid and fasterdissipation of heat; and (2) due to the plethora of concave structuresor cavities in fractal structures, the fractal heat sink is better ableto take advantage of turbulent flow mechanics than a traditional heatsink, resulting in heat entering and exiting the heat sink more quickly(3) acoustic properties, especially in forced convection systems. Thetechnology provides, according to various embodiments, a heat sink tocool an object through conduction (diffusion), convection and radiation.(See, en.wikipedia.org/wiki/Heat_transfer.)

With respect to conduction, the present technology observes that whenheat energy is conducted by phonon transport, wave phenomena arepertinent, and thus a fractal branching network can advantageously beused to reduce reflections at discontinuities and decrease compleximpedance. Further, a fractal geometry may assist in optimizing thecross-section area and surface area (for radiation and convectivetransfer) under given constraints.

With respect to convection, fractal geometry may provide acousticbenefits, by distributing acoustic energy across a wide band, and thusensuring “whiteness” of a noise spectrum and absence of sharpresonances. Further, fractal geometry may provide high or maximumsurface area, and produce turbulent cooling medium flows to reduceboundary later effects. Depending on the constraints imposed, fractalgeometry may also provide chimneys or defined flow paths through anetwork of elements, and thus control an impedance of coolant flow,though generally, a fractal branching network will produce higher flowimpedance than corresponding smooth regular surfaces. In some cases, atextured surface or configuration (as might be achieved by fractalgeometry) can actually increase laminar flow some distance away from thesurface, by creating a controlled disturbed intermediate layer.

With respect to radiation, fractal geometry can avoid parallel surfaces,which can limit radiative dissipation. For example, a parallel plateheat sink will radiatively transfer heat between the plates, and thuslimit the effectiveness of radiation from the bulk of the surfaces as aneffective dissipation mechanism. On the other hand, irregular angles andsurface branches may help to avoid reabsorption of thermal radiation bythe elements of the heat sink, and thus enhance radiative dissipation.

For the smallest heat sink elements, on the order of 10-1000 nm, thefocus of the heat transfer may be on radiation rather than convection.Electron emission and ionization may also be relevant. Larger heat sinkelements, approximately >1 mm in size, will generally rely on convectionas the primary form of heat transfer. In a fractal geometry system,elements spanning these regimes may be provided in a single system.

The heat sink may comprise a heat exchange device with a plurality ofheat exchange elements having a fractal variation therebetween. A heattransfer fluid, such as air, water, or another gas or liquid, is inducedto flow through the heat exchange device. The heat transfer fluid hasturbulent portions. The fractal variation in the plurality of heatexchange elements substantially reduces the narrow band acousticresonance resulting from fluid flow around the heat sink elements ascompared to a heat sink having a linear or Euclidian geometric variationbetween the plurality of heat exchange elements. The turbulent flow alsodisturbs the stagnant surface boundary layer, leading to more efficientheat transfer, but generally reduced flow rates for the same motiveforce. Note that, since turbulence dissipates energy, under someconditions, the heat added to the system by inducing the heat transferfluid flow can be a significant factor.

When a heat transfer fluid (air, gas, or liquid) is induced to flow overa surface, there may be turbulence in the fluid. The fractal shape ofthe heat sink would generally provide a range of physical sizeparameters, and thus for any given flow rate, would typically induceturbulent flow over some portion of a fractal geometry array. Notably,because the flow for a given heat sink may vary over a range of speeds,and the temperature and viscosity of the fluid varies over a range ofconditions, fractal geometry facilitates optimization over a range ofparameters.

In fluid dynamics, turbulence or turbulent flow is a flow regimecharacterized by chaotic property changes. This includes low momentumdiffusion, high momentum convection, and rapid variation of pressure andflow velocity in space and time. (See, en.wikipedia.org/wiki/Turbulence;www.scholarpedia.org/article/Turbulence) Flow, in which the kineticenergy dies out due to the action of fluid molecular viscosity, iscalled laminar flow. While there is no theorem relating thenon-dimensional Reynolds number (Re) to turbulence, flows at Reynoldsnumbers larger than 5000 are typically (but not necessarily) turbulent,while those at low Reynolds numbers usually remain laminar. InPoiseuille flow, for example, turbulence can first be sustained if theReynolds number is larger than a critical value of about 2040; moreover,the turbulence is generally interspersed with laminar flow until alarger Reynolds number of about 4000. In turbulent flow, unsteadyvortices appear on many scales and interact with each other. Drag due toboundary layer skin friction increases. The structure and location ofboundary layer separation often changes, sometimes resulting in areduction of overall drag. Although laminar-turbulent transition is notgoverned by Reynolds number, the same transition occurs if the size ofthe object is gradually increased, or the viscosity of the fluid isdecreased, or if the density of the fluid is increased. Turbulence ischaracterized by the following features: Irregularity: Turbulent flowsare always highly irregular. For this reason, turbulence problems arenormally treated statistically rather than deterministically. Turbulentflow is chaotic. However, not all chaotic flows are turbulent.Diffusivity: The readily available supply of energy in turbulent flowstends to accelerate the homogenization (mixing) of fluid mixtures. Thecharacteristic, which is responsible for the enhanced mixing andincreased rates of mass, momentum and energy transports in a flow, iscalled “diffusivity”.

Rotationality: Turbulent flows have non-zero vorticity and arecharacterized by a strong three-dimensional vortex generation mechanism,known as vortex stretching. In fluid dynamics, they are essentiallyvortices subjected to stretching that is associated with a correspondingincrease of the component of vorticity in the stretching direction dueto the conservation of angular momentum. In general, the stretchingmechanism implies thinning of the vortices in the directionperpendicular to the stretching direction due to volume conservation offluid elements. Thus, the radial length scale of the vortices decreasesand the larger flow structures break down into smaller structures. Theprocess continues until the small-scale structures are small enough thattheir kinetic energy can be transformed by the fluid's molecularviscosity into heat, i.e., molecular scale random motion. Turbulence isalways rotational and three dimensional.

Dissipation: To sustain turbulent flow, a persistent source of energysupply is required because turbulence dissipates rapidly as the kineticenergy is converted into internal energy by viscous shear stress. Ittherefore becomes apparent that, because turbulent flow is chaotic, anoptimization of heat sink geometry responsive to chaotic features canachieve efficiencies over a range of operating regimes, and atparticular operating regimes.

Turbulence causes the formation of eddies of many different lengthscales. Most of the kinetic energy of the turbulent motion is containedin the large-scale structures. The energy “cascades” from theselarge-scale structures to smaller scale structures by an inertial andessentially inviscid mechanism. This process continues, creating smallerand smaller structures, which produces a hierarchy of eddies. Eventuallythis process creates structures that are small enough that moleculardiffusion becomes important and viscous dissipation of energy finallytakes place. The scale at which this happens is the Kolmogorov lengthscale.

Via this energy cascade, turbulent flow can be realized as asuperposition of a spectrum of flow velocity fluctuations and eddiesupon a mean flow. The eddies are loosely defined as coherent patterns offlow velocity, vorticity and pressure. Turbulent flows may be viewed asmade of an entire hierarchy of eddies over a wide range of length scalesand the hierarchy can be described by the energy spectrum that measuresthe energy in flow velocity fluctuations for each length scale(wavenumber). The scales in the energy cascade are generallyuncontrollable and highly non-symmetric. Nevertheless, based on theselength scales these eddies can be divided into three categories.

Integral length scales: Largest scales in the energy spectrum. Theseeddies obtain energy from the mean flow and also from each other. Thus,these are the energy production eddies, which contain most of theenergy. They have the large flow velocity fluctuation and are low infrequency. Integral scales are highly anisotropic. The maximum length ofthese scales is constrained by the characteristic length of theapparatus.

Kolmogorov length scales: Smallest scales in the spectrum that form theviscous sub-layer range. In this range, the energy input from nonlinearinteractions and the energy drain from viscous dissipation are in exactbalance. The small scales have high frequency, causing turbulence to belocally isotropic and homogeneous.

Taylor microscales: The intermediate scales between the largest and thesmallest scales which make the inertial subrange. Taylor microscales arenot dissipative scale but pass down the energy from the largest to thesmallest. Taylor microscales play a dominant role in energy and momentumtransfer in the wavenumber space.

The Russian mathematician Andrey Kolmogorov proposed the firststatistical theory of turbulence, based on the aforementioned notion ofthe energy cascade (an idea originally introduced by Richardson) and theconcept of self-similarity (e.g., fractal relationships). For very highReynolds numbers, the small-scale turbulent motions are statisticallyisotropic (i.e., no preferential spatial direction could be discerned).In general, the large scales of a flow are not isotropic, since they aredetermined by the particular geometrical features of the boundaries (thesize characterizing the large scales will be denoted as L). Kolmogorovintroduced the second hypothesis: for very high Reynolds numbers thestatistics of small scales are universally and uniquely determined bythe kinematic viscosity (v) and the rate of energy dissipation (s). Withonly these two parameters, the unique length (Kolmogorov length scale)that can be formed by dimensional analysis is

$\eta = {\left( \frac{v^{3}}{\varepsilon} \right)^{1/4}.}$

A turbulent flow is characterized by a hierarchy of scales through whichthe energy cascade takes place. Dissipation of kinetic energy takesplace at scales of the order of Kolmogorov length η, while the input ofenergy into the cascade comes from the decay of the large scales, on theorder of L. These two scales at the extremes of the cascade can differby several orders of magnitude at high Reynolds numbers. In betweenthere is a range of scales (each one with its own characteristic lengthr) that has formed at the expense of the energy of the larger ones.These scales are very large compared with the Kolmogorov length, butstill very small compared with the large scale of the flow (i.e.,η<<r<<L). Since eddies in this range are much larger than thedissipative eddies that exist at Kolmogorov scales, kinetic energy isessentially not dissipated in this range, and it is merely transferredto smaller scales until viscous effects become important as the order ofthe Kolmogorov scale is approached. Within this range inertial effectsare still much larger than viscous effects, and it is possible to assumethat viscosity does not play a role in their internal dynamics (for thisreason this range is called “inertial range”). Kolmogorov theory is, atpresent, under revision. The theory implicitly assumes that theturbulence is statistically self-similar at different scales. Thisessentially means that the statistics are scale-invariant in theinertial range. However, there is evidence that turbulent flows deviatefrom this idealized behavior. See:

Davidson, P. A. (2004). Turbulence: An Introduction for Scientists andEngineers. Oxford University Press. ISBN 978-0-19-852949-1;

Falkovich, G., Scholarpedia, “Cascade and scaling”,www.scholarpedia.org/article/Cascade_and_scaling;

Jin, Y.; Uth, M.-F.; Kuznetsov, A. V.; Herwig, H. (2 Feb. 2015).“Numerical investigation of the possibility of macroscopic turbulence inporous media: a direct numerical simulation study.” Journal of FluidMechanics 766: 76-103. Bibcode:2015JFM . . . 766 . . . 76J.doi:10.1017/jfm.2015.9;

Falkovich, G., and K. R. Sreenivasan. “Lessons from hydrodynamicturbulence,” Physics Today, vol. 59, no. 4, pages 43-49 (April 2006); J.Cardy,

Falkovich. G., and K. Gawedzki (2008) Non-equilibrium statisticalmechanics and turbulence. Cambridge University Press; P. A. Durbin andB. A. Pettersson Reif. Statistical Theory and Modeling for TurbulentFlows. Johns Wiley & Sons, 2001;

Bohr, T., M. H. Jensen, G. Paladin and A. Vulpiani. Dynamical SystemsApproach to Turbulence, Cambridge University Press, 1998; J. M.McDonough (2007). Introductory Lectures on Turbulence—Physics,Mathematics, and Modeling;

Kolmogorov, Andrey Nikolaevich (1941). “The local structure ofturbulence in incompressible viscous fluid for very large Reynoldsnumbers.” Proceedings of the USSR Academy of Sciences (in Russian) 30:299-303, translated into English by V. Levin: Kolmogorov, AndreyNikolaevich (Jul. 8, 1991). Proceedings of the Royal Society A 434(1991): 9-13. Bibcode:1991RSPSA.434 . . . 9K.doi:10.1098/rspa.1991.0075;

Kolmogorov, Andrey Nikolaevich (1941). “Dissipation of Energy in theLocally Isotropic Turbulence.” Proceedings of the USSR Academy ofSciences (in Russian) 32: 16-18, translated into English by A.Kolmogorov (Jul. 8, 1991). Proceedings of the Royal Society A 434(1980): 15-17. Bibcode:1991RSPSA.434 . . . 15K.doi:10.1098/rspa.1991.0076;

Batchelor, G. K., The theory of homogeneous turbulence. CambridgeUniversity Press, 1953.)

In a fanless (passive flow) design, the main design efficiency issuesfor a given material and capacity, are size, and thermaltime-constant(s). Because such designs may operate over a range ofambient temperatures, they are typically over-provisioned for the normaloperating case. The typical heat transfer medium flow rates available insuch a design rarely reach a range to cause significant turbulence, andindeed, the design typically provides flow channels which seek tomaintain laminar flow to ensure convective transfer over a large area ofthe heat sink with minimum acoustic emission that would arise fromturbulence. In order to increase efficiency, the present technologyincreases surface area through patterning of surfaces, and seeks todiminish laminar flow boundary layer thickness by initiating vorticesand other turbulent effects at relatively low flow rates as might becharacteristic of passive thermally induced convection in a heattransfer fluid, such as air.

According to another aspect, the apertures serve to increase surfacearea at low flow rates, and increase turbulence at high flow rates, thusproviding two distinct operational regimes.

According to these precepts, the heat sink design can maintain a thinboundary layer over a significant portion of the surface, over a widerange of heat transfer medium flow conditions. In typical prior artdesigns, the surfaces are subject to the same constraints, and at lowflow rates, a thick boundary layer is present, at a design nominal flowrate, an optimum heat transfer efficiency is obtained, with acorresponding thin boundary layer, while at higher flow rates there is aloss of efficiency due to separation of the turbulent boundary layerfrom the surface, resonances and acoustic emissions, exponentialincrease in flow resistance, etc. Typically, a fan is provided, whichmay have a speed control, though in some cases the fan operates atconstant speed. (Fixed fan speeds are useful, for example, in datacenterimplementations, where the fans are provided to ensure unidirectionalflow without risk of reverse flows).

On the other hand, according to the present technology, the optimum heattransfer conditions are distributed across a larger flow rate range,with the characteristic that the heat transfer efficiency can varylocally as a function of flow conditions. At peak load conditions, onenaturally seeks relatively low flow impedance and high flow rates, butmay also tolerate increased turbulence and accompanying noise.

With the multilevel fractal design, multiscale turbulence is generated.Multiscale turbulence is a class of flows in which the chaotic motion ofthe fluid is forced at different length and/or time scales.

See, en.wikipedia.org/wiki/Turbulence,

en.wikipedia.org/wiki/Multiscale turbulence.

Laizet, S., Vassilicos, J. C. (January 2009). “Multiscale Generation ofTurbulence”. Journal of Multiscale Modelling. 01 (01): 177-196.doi:10.1142/S1756973709000098;

Mazzi, B.; Vassilicos, J. C. (10 Mar. 2004). “Fractal-generatedturbulence”. Journal of Fluid Mechanics. 502: 65-87.doi:10.1017/S0022112003007249.

This may be achieved by immersing in a moving fluid a body with amultiscale, often fractal-like, arrangement of length scales. Thisarrangement of scales can be either passive (Hurst, D.; Vassilicos, J.C. (2007). “Scalings and decay of fractal-generated turbulence”. Physicsof Fluids. 19 (3): 035103. doi:10.1063/1.2676448; Nagata, K.; Sakai, Y.;Inaba, T.; Suzuki, H.; Terashima, O.; Suzuki, H. (2013). “Turbulencestructure and turbulence kinetic energy transport inmultiscale/fractal-generated turbulence”. Physics of Fluids. 25 (6):065102. doi:10.1063/1.4811402), or active (Thormann, A.; Meneveau, C.(February 2014). “Decay of homogeneous, nearly isotropic turbulencebehind active fractal grids”. Physics of Fluids. 26 (2): 025112.doi:10.1063/1.4865232). Three examples of multiscale generators, includea fractal cross grid, a fractal square grid and a fractal I grid.en.wikipedia.org/wiki/Turbulence.

Boschung, J., et al. “Streamlines in stationary homogeneous isotropicturbulence and fractal-generated turbulence.” Fluid Dynamics Research48.2 (2016): 021403.

Cafiero, Gioacchino, et al. “Flow field features of fractal impingingjets at short nozzle to plate distances.” Experimental Thermal and FluidScience 78 (2016): 334-344.

Cafiero, Gioacchino, Stefano Discetti, and Tommaso Astarita. “Flow fieldtopology of submerged jets with fractal generated turbulence.” Physicsof Fluids 27.11 (2015): 115103.

Cafiero, Gioacchino, Stefano Discetti, and Tommaso Astarita. “Heattransfer enhancement of impinging jets with fractal-generatedturbulence.” International Journal of Heat and Mass Transfer 75 (2014):173-183.

Cheskidov, Alexey, Charles R. Doering, and Nikola P. Petrov. “Energydissipation in fractal-forced flow.” Journal of mathematical physics48.6 (2007): 065208.

Coffey, C. J., et al. “Mixing effectiveness of fractal grids for inlinestatic mixers.” Proof of Concept Report for the Attention of ImperialInnovations. www3. imperial. ac. uk/tmfc/papers/poc (2007).

Coppola, G., and A. Gomez. “Experimental investigation on a turbulencegeneration system with high-blockage plates.” Experimental Thermal andFluid Science 33.7 (2009): 1037-1048.

Dairay, T., M. Obligado, and J. C. Vassilicos. “Non-equilibrium scalinglaws in axisymmetric turbulent wakes.” Journal of Fluid Mechanics 781(2015): 166-195.

Discetti, S., et al. “PIV study of fractal grid turbulence.” 9thInternational Symposium on Particle Image Velocimetry-PIV. Vol. 11.2011.

Fragner, Romain, et al. “Multi-scale high intensity turbulence generatorapplied to a high pressure turbulent burner.” Flow, Turbulence andCombustion 94.1 (2015): 263-283.

Gomes-Fernandes, R., B. Ganapathisubramani, and J. C. Vassilicos.“Particle image velocimetry study of fractal-generated turbulence.”Journal of Fluid Mechanics 711 (2012): 306-336.

Hampp, F., and R. P. Lindstedt. “Fractal Grid Generated Turbulence—ABridge to Practical Combustion Applications.” Fractal Flow Design: Howto Design Bespoke Turbulence and Why. Springer International Publishing,2016. 75-102.

Hearst, R. Jason, and Philippe Lavoie. “Decay of turbulence generated bya square-fractal-element grid.” Journal of Fluid Mechanics 741 (2014):567-584.

Hearst, R. Jason, and Philippe Lavoie. “Scale-by-scale energy budget infractal element grid-generated turbulence.” Journal of Turbulence 15.8(2014): 540-554.

Hearst, Robert Jason, and Philippe Lavoie. “Velocity derivative skewnessin fractal-generated, non-equilibrium grid turbulence.” Physics ofFluids 27.7 (2015): 071701.

Hurst, D., and J. C. Vassilicos. “Scalings and decay offractal-generated turbulence.” Physics of Fluids 19.3 (2007): 035103.

Keylock, C. J., et al. “The flow structure in the wake of a fractalfence and the absence of an “inertial regime”.” Environmental fluidmechanics 12.3 (2012): 227-250.

Krogstad, P-Å., and P. A. Davidson. “Freely decaying, homogeneousturbulence generated by multi-scale grids.” Journal of Fluid Mechanics680 (2011): 417-434.

Krogstad, Per-Åge. “Turbulent decay in the near field of multi-scale andconventional grids.” International Journal of Heat and Fluid Flow 35(2012): 102-108.

Laizet, S., and J. C. Vassilicos. “Multiscale generation of turbulence.”Journal of Multiscale Modelling 1.01 (2009): 177-196.

Laizet, S., and J. C. Vassilicos. “Stirring and scalar transfer bygrid-generated turbulence in the presence of a mean scalar gradient.”Journal of Fluid Mechanics 764 (2015): 52-75.

Laizet, S., and J. Christos Vassilicos. “Direct numerical simulation offractal-generated turbulence.” Direct and Large-Eddy Simulation VII(2010): 17-23.

Laizet, S., E. Lamballais, and J. C. Vassilicos. “A numerical strategyto combine high-order schemes, complex geometry and parallel computingfor high resolution DNS of fractal generated turbulence.” Computers &Fluids 39.3 (2010): 471-484.

Laizet, S., Y. Sakai, J. C. Vassilicos, “Turbulent flowsgenerated/designed in multiscale/fractal ways: fundamentals andapplications”, 1ST UK-Japan Bilateral WorkshoP, 28-29 Mar. 2011,Department of Aeronautics, Imperial College London.

Laizet, Sylvain, and John Christos Vassilicos. “DNS of fractal-generatedturbulence.” Flow, turbulence and combustion 87.4 (2011): 673-705.

Laizet, Sylvain, and Ning Li. “Incompact3d: A powerful tool to tackleturbulence problems with up to 0 (105) computational cores.”International Journal for Numerical Methods in Fluids 67.11 (2011):1735-1757.

Laizet, Sylvain, et al. “Low Mach number prediction of the acousticsignature of fractal-generated turbulence.” International Journal ofHeat and Fluid Flow 35 (2012): 25-32.

Laizet, Sylvain, J. C. Vassilicos, and Claude Cambon. “Interscale energytransfer in decaying turbulence and vorticity-strain-rate dynamics ingrid-generated turbulence.” Fluid Dynamics Research 45.6 (2013): 061408.

Laizet, Sylvain, J. Nedić, and J. Christos Vassilicos. “The spatialorigin of −5/3 spectra in grid-generated turbulence.” Physics of Fluids27.6 (2015): 065115.

Manshoor, Bukhari bin, F. C. G. A. Nicolleau, and S. B. M. Beck. “Thefractal flow conditioner for orifice plate flow meters.” Flowmeasurement and Instrumentation 22.3 (2011): 208-214.

Mazellier, Nicolas, and J. C. Vassilicos. “The turbulence dissipationconstant is not universal because of its universal dependence onlarge-scale flow topology.” Physics of Fluids 20.1 (2008): 015101.

Mazellier, Nicolas, and J. C. Vassilicos. “Turbulence withoutRichardson-Kolmogorov cascade.” Physics of fluids 22.7 (2010): 075101.

Mazellier, Nicolas, Luminita Danaila, and Bruno Renou. “Multi-scaleenergy injection: a new tool to generate intense homogeneous andisotropic turbulence for premixed combustion.” Journal of Turbulence 11(2010): N43.

Mazzi, B., and John Christos Vassilicos. “Fractal-generated turbulence.”Journal of Fluid Mechanics 502 (2004): 65-87.

Meldi, Marcello, Hugo Lejemble, and Pierre Sagaut. “On the emergence ofnon-classical decay regimes in multiscale/fractal generated isotropicturbulence.” Journal of Fluid Mechanics 756 (2014): 816-843.

Melina, G., P. J. K. Bruce, and J. C. Vassilicos. “Vortex sheddingeffects in grid-generated turbulence.” Physical Review Fluids 1.4(2016): 044402.

Nedić, J., et al. “Aeroacoustic performance of fractal spoilers.” AIAA J50.12 (2012): 2695-2710.

Nedic, Jovan. “Fractal-generated wakes.” (2013).

Nicolleau, F. C. G. A. “Return to axi-symmetry for pipe flows generatedafter a fractal orifice.” Fluid Dynamics Research 45.6 (2013): 061402.

Oberlack, Martin, and Andreas Rosteck. “New statistical symmetries ofthe multi-point equations and its importance for turbulent scalinglaws.” Discrete Contin. Dyn. Syst. Ser. S 3.3 (2010): 451-471.

Oberlack, Martin, and George Khujadze. “Fractal-generated turbulentscaling laws from a new scaling group of the multi-point correlationequation.” TSFP DIGITAL LIBRARY ONLINE. Begel House Inc., 2009.

Othman, Mohd Fahmi, Bukhari Manshoor, and Amir Khalid. “Circle gridfractal plate as a turbulent generator for premixed flame: an overview.”IOP Conference Series: Materials Science and Engineering. Vol. 50.No. 1. IOP Publishing, 2013.

Rakhshandehroo, G. Reza, et al. “Temporal variation of velocitycomponents in a turbulent open channel flow: Identification of fractaldimensions.” Applied Mathematical Modelling 33.10 (2009): 3815-3824.

Schneemann, Jorge, et al. “Lift measurements in unsteady flowconditions.” Proceedings of EWEC. 2010.

Seoud, R. E. E., and J. C. Vassilicos. “Passive multiscale flow controlby fractal grids.” IUTAM Symposium on Flow Control and MEMS. SpringerNetherlands, 2008.

Seoud, R. E., and J. C. Vassilicos. “Dissipation and decay offractal-generated turbulence.” Physics of Fluids 19.10 (2007): 105108.

Stresing, R., et al. “Defining a new class of turbulent flows.” Physicalreview letters 104.19 (2010): 194501.

Stresing, R., et al. “Stochastic Analysis of Turbulence n-ScaleCorrelations in Regular and Fractal-Generated Turbulence.” Progress inTurbulence III. Springer, Berlin, Heidelberg, 2009. 49-52.

Stresing, Robert, and J. Peinke. “Towards a stochastic multi-pointdescription of turbulence.” New Journal of Physics 12.10 (2010): 103046.

Suzuki, Hiroki, et al. “Fractal analysis of turbulent mixing infractal-generated turbulence by planar laser-induced fluorescence.”Physica Scripta 2013.T155 (2013): 014062.

Sykes, R. I., and R. S. Gabruk. “Fractal representation of turbulentdispersing plumes.” Journal of Applied Meteorology 33.6 (1994): 721-732.

Valente, P. C., and J. C. Vassilicos. “Dependence of decayinghomogeneous isotropic turbulence on inflow conditions.” Physics LettersA 376.4 (2012): 510-514.

Valente, P. C., and J. C. Vassilicos. “The energy cascade ingrid-generated non-equilibrium decaying turbulence.” Physics of Fluids27.4 (2015): 045103.

Valente, P. C., and J. C. Vassilicos. “The non-equilibrium region ofgrid-generated decaying turbulence.” Journal of Fluid Mechanics 744(2014): 5-37.

Valente, P. C., and John Christos Vassilicos. “The decay of turbulencegenerated by a class of multiscale grids.” Journal of Fluid Mechanics687 (2011): 300-340.

Van Melick, P. A. J., and B. J. Geurts. “Flow through a cylindrical pipewith a periodic array of fractal orifices.” Fluid dynamics research 45.6(2013): 061405.

Vassilicos, J. Christos. “Dissipation in turbulent flows.” Annual Reviewof Fluid Mechanics 47 (2015): 95-114.

Weitemeyer, Stefan, et al. “Multi-scale generation of turbulence withfractal grids and an active grid.” Fluid Dynamics Research 45.6 (2013):061407.

Zheng, H. W., F. C. G. A. Nicolleau, and N. Qin. “Detached eddysimulation for turbulent flows in a pipe with a snowflake fractalorifice.” New Approaches in Modeling Multiphase Flows and Dispersion inTurbulence, Fractal Methods and Synthetic Turbulence. SpringerNetherlands, 2012. 9-21.

Laizet, S., and J. C. Vassilicos. “Multiscale generation of turbulence.”Journal of Multiscale Modelling 1.01 (2009): 177-196 (supra,incorporated by reference) states:

-   -   . . . for a particular class of fractal grids, i.e., the fractal        square grids, two regions exist downstream of the grid: a        turbulence production region followed by a turbulence        dissipation region where the turbulence is statistically        homogeneous and isotropic. Other families of fractal grids        behave differently on the centreline and do not exhibit a        progressive turbulence build-up downstream of the grid on the        centreline. The various velocity profiles, correlations, spectra        and coherence spectra in the free decay region indicate that the        turbulence is homogeneous and isotropic to a satisfactory        approximation there. Yet, remarkably, the integral and Taylor        length scales remain constant during decay downstream of fractal        square grids (as opposed to classical mesh grids, where they        markedly increase, and fractal cross and I grids on the        centreline, where they also increase). The most recent        experiments on turbulence generated by fractal square grids        indicate that the kinetic energy dissipation scales as Rλ-1 (Rλ        is the Reynolds number based on Taylor's micro-scale) over the        range from O(100) to O(1000) and reaches values that are an        order of magnitude smaller than in any approximately isotropic        turbulence experiment to date. However, the flow is fully        turbulent with an energy spectrum that has a clear −5/3 range.        There is also intriguing evidence that the interscale energy        transfers are severely modified in fractal-generated turbulence        even very far downstream. These properties are completely        different from those of any turbulent flow studied to date and        run counter to the classical views on turbulence stemming from        Taylor and Kolmogorov, who set the foundations of modern        turbulence research. In particular, all modelling approaches and        all theories of turbulence assume that the kinetic energy        dissipation rate is independent of Rλ. These unprecedented        results indicate that the turbulence in flows past fractal        objects cannot be modelled using any of the existing and/or        conventional approaches.    -   Moreover, fractal grids can be designed as stirring elements for        inline static mixers and, as shown by recent proof-of-concept        experiments, they compare favourably with commercially available        state-of-the-art stirring elements. This has been achieved        without time for optimisation and adaptation. Hence,        possibilities for improvement are vast, with the potential to        set new industrial mixing standards, at least for some mixing        applications.

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56. S. Ferrari and L. Rossi, Particle tracking velocimetry andaccelerometry (PTVA) mea-surements applied to quasi-two-dimensionalmultiscale flows, Exp. Fluids 44 (2008) 873-886.

57. A. Tsinober, E. Kit and T. Dracos, Experimental investigation of thefield of velocity gradients in turbulent flows, J. Fluid Mech. 242(2008) 169-192.

58. K. Nagata, H. Suzuki, Y. Sakai, T. Hayase and T. Kubo, Directnumerical simulation of turbulent mixing in grid-generated turbulence,Phys. Scripta (2008), in press.

Fractal grids can be used as mixers to design turbulent flows with lowpower losses and high turbulence intensities for intense yet economicmixing over a region of designed length and location. The fractal mixermay be provided ahead of a heat sink, to generate turbulence in the airflow impinging on the heat sink, or may be generate by the heat sink,such as by fractal-apertured surfaces which form the heat sink.

In this set of embodiments shown in FIGS. 15, and 34-27 , the fractalgrid (or in the case of FIG. 15 , the 3D fractal filter), the fractalgrid may be separate from, or integral with, the heat sink. A coolingfan may be provided adjacent to the heat sink, within a shroud, with afractal grid within the flow path between the fan blades and the heatsink. In another embodiment, as shown in FIGS. 38-40 , the fractal gridforms part of a heat dissipative plate which forms part of the heatsink, and interacts with a flow of air. In some cases, the optimumspatial configuration of the heat sink may change as a function oftemperature. In that case, a shape memory alloy or bimetallic elementmay be provided as part of a support for the plate (or fin, or pin, orother structure), which changes a distance or angle as a function oftemperature. In the case of a shape memory alloy, the change(s) willoccur abruptly, and permits defining discrete temperature range(s) forparticular configurations; in the case of bimetallic elements, thechange occurs continually. See,en.wikipedia.org/wiki/Shape-memory_alloy;en.wikipedia.org/wiki/Bimetallic strip. The effect of the fractal gridsis to efficiently increase turbulence with lower blockage ratios, ascompared to regular (non-fractal) patterns.

The prior fractal grids are typically regular and symmetric, butaccording to the present technology, need not be. For example, if theheat sink is an irregular fractal design, the optimal grid will notnecessarily be regular and symmetric. Similarly, where the fractalpattern is provided as part of the heat sink, the optimal patterncharacteristics will vary as a function of distance from the root orheat source or branch point/line/feature. Typically, the fractal naturewill extend over a limited number of orders or scales. For example, theself-similarity may extend over a range of 2-12 orders, with each orderbeing, for example, a factor of 1.1 to about 2. For example, in a 2order design, the scale factor will tend toward 1.5-2, while in a higherorder design, the scale factor will tend toward 1.2 to 1.8. Of course,the scale factor may be any such factor within the range, e.g., 1.1,1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, ˜2.0, and any value in between.Typically, the scales will be the same between orders in a regularsymmetric design, but may in fact vary over order and regionally withinthe system. Often, the basic design is generated using an iteratedfunction, however, in a practical manufactured system, somesimplifications, quantized values, and estimates or approximations maybe employed. Thus, a feasible manufactured produce may deviate somewhatfrom the algorithmically optimized design, without departing from thespirit or scope of the invention. For purposes of this disclosure, adesign according to an algorithm is one which deviates less than 10%full scale from the algorithmic optimum, and which avoids altering themaximum heat transfer capacity by diminution of more than 20%,Similarly, in some cases, boundary constraints are not fully calculatedby the generative algorithm, the produce may provide 50% of surfaces andconfiguration which correspond to the generative algorithm. For example,the coupling of a heat sink to a heat source will typically beconstrained to provide a regular, solid interface region, and thealgorithm would generally not seek to define the mechanical interfaceregions. Likewise, the surface texture or perforation pattern defined byan algorithm may be independent of spatial constraints, and therefore asthe pattern approaches any such constraint, the conformance with thepattern may be attenuated or ceased.

According to the design, a gross morphology may be defined, and asurface configuration imposed on the gross morphology that increaseefficiency in some significant way, with significantly defined here asbeing greater than 2.5% of the metric. However, the morphology andsurface may be interactively optimized. For example, the morphology mayprovide relatively large channels for heat transfer medium flows. Thesechannels may serve to direct the flow toward a fractal or multiscalepattern, which then alters the flow pattern at that pattern and in theflows downstream from that pattern. Similarly, the fractal or multiscalepattern may generate vibrations or noise, which can then couple withportions of the morphology. While in most cases, resonant vibration ofthe body of the heat sink is undesirable, in other cases this may beacceptable and indeed a means to increase efficiency. For example, in abranched design as shown in FIGS. 22 and 38-45 , a vibration at the tipsof the heat exchange elements may increase heat transfer efficiency, andthis may be induced by fluid dynamic effects remote from the tips.Meanwhile, if the tips can be designed or controlled to vibrate inantiphase, the net acoustic and vibrational output may be mitigated.

The heat sink may have thermal and/or air flow sensors on the surface,to measure or estimate heat or heat transfer medium flow effects. Thesemay be wired, wireless, or optical-detection designs. For example, undera certain load, a model-based controller may indicate that turbulentflows are desired at a certain region of the heat sink in order to meetoperational goals, which may reflect heat source temperature, operatingefficiency, etc. The sensors may be used to control fan speed, or in thecase of a controllable or adaptive fractal grid or surface, certaincharacteristics or parameters of the grid or surface. For example, anopen space ratio may be altered by a mechanical transducer. On the otherhand, if the fractal or multiscale structure is provided near to a fan,the structures will interact. This interaction may be unpredictable orpoorly predictable, and feedback may help stabilize and optimize theoperation.

The system may employ a dynamically varying bulk flow of heat transfermedium, e.g., from a fan whose speed is substantially modulated, forexample over a range of at least ±15%, more preferably ±20%, and mostpreferably ±50%. The goal of this variation is, with equivalent fanpower consumption, to generate high peak flows that more efficiency shedheat from the surfaces than a static flow rate. Preferably, at the peakflow rate, turbulence occurs, while generally it will be significantlydiminished, e.g., >10%, at the lower flow rate. While the fan can intheory be stopped, providing maximum ratio, in practice the startupcurrent of the fan motor will reduce efficiency, and the cycle time maybe rapid enough that waiting for the fan to stop rotating would beinefficient. The fan may run continuously or intermittently, or withchanging speed over time, and a deflector may be provided to dynamicallyvary the flows with respect to the heat sink.

In general, at heat loads below 50% of peak, the system may be moreefficient or quieter if it avoids turbulent flows, and adopts a moretraditional heat sink operating regime at low heat loads. On the otherhand, by increasing peak efficiency at high loads, the heat sink may berelatively smaller, lighter, higher capacity, or less expensivematerials, than more traditional designs. In general, the present designheat sinks are mechanically more complex than traditional heat sinks,and may in some embodiments have control systems which are more complex.However, the relationship between heat sink complexity and cost may beweak. On the other hand, in the case of copper or more exotic materials,the material cost may be a significant factor, and outweigh mechanicalcomplexity as a design or feasibility constraint.

The fractal or multiscale nature of the heat sink, at one of multiplelevels, may be used to enhance the turbulent nature of flows, andtherefore enhancing heat transfer, with low energy loss and reduced sizeas compared to the parallel plate design.

Therefore, the efficiency of heat transfer may be increased as comparedto a heat exchange device having a linear or Euclidian geometricvariation between several heat exchange elements, at least over certainregimes of operation. This is achieved by the efficient generation ofturbulent flows, which disrupt the surface boundary layer of the heatsink, leading to enhanced heat transfer. The fractal design producesefficient multiscale turbulence at small size and low energydissipation. The turbulent flow may be induced in the stream of heattransfer medium before reaching the heat sink, such as with a multiscalefilter, which has the property of organizing the turbulence, ascompared, for example, to a jet. See, Dimotakis, Paul E., and Catrakis,Haris J., “Turbulence, fractals, and mixing”, GALCIT Report FM97-1, Jan.17, 1997 (Turbulent flow, or turbulence, is found to have two importantand interrelated properties. It is chaotic and it can transport, stir,and mix its constituents with great effectiveness. By chaotic, we meanthat it is characterized by irregular temporal and spatial dynamics thatare unstably related to its initial and boundary conditions. The RandomHouse Dictionary of the English Language (1971), for example, offers asa definition of turbulent flow, “The flow of a fluid past an object suchthat the velocity at any fixed point in the fluid varies irregularly.”)

The heat exchange device may include a highly conductive substance whoseheat conductivity exceeds 850 W/(m·K). Examples of such superconductorsinclude graphene, diamond, and diamond-like coatings. Alternatively, theheat exchange device may include carbon nanotubes. At such high thermalconductivities, phonon heat transport may be at play.

A heat sink according to the present technology may be manufactured, forexample, as a 3D print or as a casting. Further, a cast design may beproduced by an investment casting (e.g., lost wax or lost foam design)from a 3D printed form or template. Thus, in practice, a design isgenerated on a computer-aided design (CAD) system, which may, forexample, employ algorithms to optimize the shape according to variouscriteria, such as size, weight, heat load, air flow, other convectiveheat transfer parameters, infrared radiation recapture, and othercriteria. The design is then converted, by a computer assistedmanufacturing (CAM) system, such as an additive manufacturing “3D”printer or 2.5D printer (layers), into a form. The form, if producedusing a metal sintering or ceramic process, may itself be a heat sink,though more typically the form is a polymer, which can then be used tocreate a mold. The mold, in turn, can be used to create multipletemplates, which can be used in a casting process. Relatively complexmechanical designs can thus be replicated in volume. The molded metalmay be heterogeneous, resulting in a range of properties over differentregions of the mold. As discussed above, a small-scale set of featuresmay be provided by using a coating technology, especially one whichprovides self-organizing features. The distribution of the small-scalefeatures may be controlled by the deposition technology, by thecharacteristics/shape of the surface upon which the coating is beingapplied, or by a spatially selective manufacturing process.

The design may result in a fractal shape, e.g., with branches ormultiple levels of branches, with multiple characteristic scales, whichmay have some symmetries or repetitions, or be absent symmetries andrepetitions. A design which is self-similar at various scales, isconsidered “fractal”. Some fractals avoid exact replication ofstructures (e.g., having asymmetric structures), while others lack anysuch asymmetries (e.g., having symmetric structures). A design whichadopts some of these characteristics, or functionally emulates some ofthese characteristics, is considered “fractal-like”. A designrepresenting an array of uniform, repeating elements of the same scaleis generally considered non-fractal. In some cases, a branching arrayhaving multi-directional symmetry may in some cases be consideredfractal-like. A multiscale fractal (i.e., with asymmetries within eachscale range) with outwardly tapering branches will tend to carry anddissipate heat further from the heat source than a symmetric design,since by nature the larger cross section branches will carry heatfurther than their smaller, higher-surface-area-per mass cousinbranches, and the asymmetry will tend to assure that some branchesindeed have larger cross sections; however, this is not the only effectto be obtained. Since the fractal is typically generated by an iterativefunction system (IFS) responsive to its local environment, the fractalmay be optimized by a steering function to steer heat flow to areas withhighest convective heat loss, while avoiding heat flow toward brancheswhich do not efficiently shed heat. Similarly, in a vacuum heat sinkemitter, the heat loss tends to be radiative, and the optimization canaddress maximization of net radiative heat loss within the constrainedenvironment.

A fractal heat sink design does not have to be limited to a singlefractal algorithm. Multiple independent fractal algorithms can be used.One branching fractal algorithm may be used to control three-dimensionalbranching structure of the heat sink, while another fractal algorithmdetermines two-dimensional surface of the branches. For example, atwo-dimensional fractal structure may include holes arranged in afractal pattern punctured in the blades to form, for example aSierpinski carpet or another fractal pattern. Or such two-dimensionalalgorithm can control the texture of the blades in the branchingstructure. Alternatively, a two-dimensional fractal algorithm cancontrol branching of channels for passing cooling fluid within theblades of the branching structure. Multiple fractal algorithmsco-existing in one object are often found in nature. Thus, a tree leafmay have one fractal algorithm that determines the shape of the leaf andanother fractal algorithm that determines the branching of veins in theleaf. In a human or animal organ, one fractal algorithm may determinethe shape of the organ; another fractal algorithm may determine thebranching structure of blood vessels; yet another fractal algorithmdetermines distribution of lymphatic vessels; still another fractalalgorithm determines distribution of nerves in the organ, etc. Some ofthese fractal systems may be competing for resources. In a tree leaf,for example, the larger the area of the leaf, the more sunlight the leafcan absorb for photosynthesis but, on the other hand, the larger thearea, the more liquid the plant is going to lose through evaporation.Competing fractal algorithms may ultimately determine the shape of theleaf or morphology of an organ. Similarly, in designing a heatexchanger, multiple and competing fractal algorithms may be used,wherein an optimization may be sought across multiple parameters. Forexample, increasing surface area increases heat loss through convectionand radiation. At the same time, it increases dust accumulation, whichmay depresse heat loss through convection and radiation as compared toan optimized surface. This consideration militates in favor of designinga heat sink with three-dimensional branching structure following onefractal algorithm and puncturing holes, arranged in a fractal pattern,through the blades following another two-dimensional fractal algorithm.

Various variations on this heat sink will be apparent to skilled personsin the art. For example, the heat sink could include a heat transfersurface that is connected to the heat exchange device and is designed toaccept a solid to be cooled. Alternatively, there could be a connectorthat is designed to connect with a solid to be cooled in at least onepoint. There may be at least three connectors serving to keep the solidand the heat sink in a fixed position relative to one another. Variousconnectors will be apparent to persons skilled in the art. For example,the connector could be a point connector, a bus, a wire, a planarconnector or a three-dimensional connector. The heat sink may have acentral aperture or void designed to accept a solid to be cooled. Theheat sink may also be integral to the heat source, or attached by othermeans.

This heat sink is typically intended to be used to cool objects, and maybe part of a passive or active system. Modern three-dimensional laserand liquid printers can create objects such as the heat sinks describedherein with a resolution of features on the order of about 16 μm, makingit feasible for those of skilled in the art to use such fabricationtechnologies to produce objects with a size below 25 cm. Alternatively,larger heat sinks, such as car radiators, can be manufactured in atraditional manner, designed with an architecture of elements having afractal configuration. For example, a liquid-to-gas heat exchanger(radiator) may be provided in which segments of fluid flow conduit havea fractal relationship over three levels of recursion, i.e., paths withan average of at least two branches. Other fractal design concepts maybe applied concurrently, as may be appropriate.

The heat sink may comprise a heat exchange device having a plurality ofheat exchange elements having a fractal variation there-between, forcooling a solid interfaced with the heat sink. A heat transfer fluidhaving turbulent portions is induced to flow with respect to theplurality of heat exchange elements. The fractal variation in theplurality of heat exchange elements serves to substantially reducenarrow band resonance as compared to a corresponding heat exchangedevice having a linear variation between a plurality of heat exchangeelements.

A preferred embodiment provides a surface of a solid heat sink, e.g., aninternal or external surface, having fluid thermodynamic propertiesadapted to generate an asymmetric pattern of vortices over the surfaceover a range of fluid flow rates. For example, the range may comprise arange of natural convective fluid flow rates arising from use of theheat sink to cool a heat-emissive object. The range may also comprise arange of flow rates arising from a forced convective flow (e.g., a fan)over the heat sink.

The heat sink may cool an unconstrained or uncontained fluid, generallyover an external surface of a heat sink, or a constrained or containedfluid, generally within an internal surface of a heat sink.

It is therefore an object of the present invention to provide a heatsink system comprising: a base structure configured to interface with aheat source; a heat exchange device configured to receive heat from thebase structure, and emit the received heat from a heat exchange surface,into an external surrounding heat exchange medium, said heat exchangedevice having generally fractal geometry with multiple independentfractal algorithms.

It is another object to provide a heat sink comprising: a heattransmissive body, having a base configured to receive a heat load, anda three dimensional configuration having an external surface configuredto transfer a heat load corresponding to the heat load received by thebase to an external heat transfer fluid; and a multiscale patternassociated with the external surface, the multiscale pattern having atleast three orders over a range of at least at least three, themultiscale pattern being distinct from the three dimensionalconfiguration, wherein the multiscale pattern is configured to disrupt aflow of the external heat transfer fluid at the external surface toreduce a stagnant surface layer to facilitate heat transfer.

The heat sink may further comprise a fan, configured to induce the flowof the external heat transfer fluid.

The multiscale pattern may be integral with, or separate from, theexternal surface. The multiscale pattern may comprise a fractal grid.The multiscale pattern may comprise a 3D fractal filter. The multiscalepattern may comprise a perforation pattern of the external surface. Themultiscale pattern may comprise a fractal texture. The multiscalepattern may comprise a 3D relief pattern on the external surface. Themultiscale pattern may be configured to induce a turbulent flow of theexternal heat transfer fluid prior to interacting with the externalsurface. The multiscale pattern may be configured to induce a turbulentflow of the external heat transfer fluid while interacting with theexternal surface.

The three-dimensional configuration may have a multiscale pattern. Themultiscale pattern may be defined by a first algorithm and thethree-dimensional configuration is defined by a second algorithm, thefirst and second algorithms being respectively independently defined.The multiscale pattern may be defined by a first fractal generativealgorithm and the three-dimensional configuration is defined by a secondfractal generative algorithm, the first and second algorithms beingrespectively different. The three-dimensional configuration may have aprogression of at least two orders of branches, wherein an aggregatecross section area after the first order of branches is less than across section area prior to the first order of branches, and anaggregate cross section area after the second order of branches is lessthan a cross section area prior to the second order of branches. Thethree-dimensional configuration and multiscale pattern may be optimizedaccording to a Computational Flow Dynamics model of the external heattransfer fluid. The three-dimensional configuration and multiscalepattern may be optimized using a genetic algorithm to supply parametersof a generative algorithm for each of the three dimensionalconfiguration and the multiscale pattern.

It is another object to provide a heat sink comprising: a baseconfigured to transfer a heat load; a heat transmissive body, having thebase, and a three dimensional configuration corresponding to a firstalgorithm with a plurality of heat exchange surfaces; and a multiscalepattern associated with the plurality of plurality of heat exchangesurfaces configured to transfer a heat load corresponding to the heatload transferred to the base, to a heat transfer fluid, the multiscalepattern corresponding to a second algorithm different from the firstalgorithm, wherein the first layout algorithm and the second layoutalgorithm are together optimized responsive to both a predicted heattransfer capacity over a range of heat transfer fluid flows.

It is a further object to provide a heat sink comprising: a baseconfigured to transfer a heat load; a heat transmissive body, having thebase, having a three dimensional configuration corresponding to a firstalgorithm; and a multiscale perforation or surface relief pattern of asurface of the heat transmissive body, configured to transfer the heatload to a heat transfer fluid, the multiscale pattern corresponding to asecond algorithm, wherein the first layout algorithm and the secondlayout algorithm are optimized responsive to both a predicted heattransfer capacity over a range of heat transfer fluid flows.

It is another object to provide a heat sink comprising a thermallyconductive body having a topologically branched three dimensionalconfiguration defining a plurality of heat exchange surfaces configuredto transfer a heat load from the thermally conductive body to a heattransfer fluid surrounding the plurality of heat exchange surfaces, theplurality of heat exchange surfaces each having a multiscale pattern,the multiscale pattern of a first surface of the heat exchange surfacesbeing configured to induce a turbulent flow of the heat transfer fluidat a second surface of the heat exchange surfaces over a range of heattransfer fluid flow conditions.

It is another object to provide a heat-exchange device, comprising aplurality of heat-exchange elements arranged in a three-dimensionalspace in a first fractal configuration, each said heat-exchange elementhaving a surface texture arranged in a second fractal configuration. Thefirst fractal configuration may be a 2D fractal extended in a thirddimension. The first fractal configuration may be, e.g.,

-   -   an L-system (en.wikipedia.org/wiki/L-system);    -   a Quadratic Koch Island        (paulbourke.net/fractals/quadratic_koch_island_a/, Addison, Paul        S., Fractals and Chaos: An illustrated course, Institute of        Physics Publishing 1997),    -   a Koch Snowflake (en.wikipedia.org/wiki/Koch snowflake), a        modified Koch Snowflake, an Icosahedron flake        en.wikipedia.org/wiki/N-flake),    -   an Octahedron flake, a fractal canopy        (en.wikipedia.org/wiki/Fractal canopy),    -   a fractal tree (e.g., en.wikipedia.org/wiki/H_tree),    -   a fractal grid (e.g.,        en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension),    -   a Sierpinski Triangle        (en.wikipedia.org/wiki/Sierpinski_triangle),    -   a Sierpinski Carpet (en.wikipedia.org/wiki/Sierpinski_carpet),    -   a Sierpinski tetrahedron,    -   a Dodecaedron fractal (commons.wikimedia.org/wiki/Fractal,        www.georgehart.com/rp/polyhedra-clusters/Polyhedra-Clusters.html),    -   a Cantor set (en.wikipedia.org/wiki/Cantor_set),    -   Cantor dust,    -   3D Cantor dust,    -   a branching tree, or    -   a Peano curve (en.wikipedia.org/wiki/Peano_curve).

The second fractal configuration may comprise

-   -   Cantor dust,    -   a crinkled canopy        (www.iasefmdrian.com/cricnkled-canopy-random-fractal),    -   a Koch surface (robertdickau.com/kochsurface.html), or    -   a Triangular Koch fractal surface,

for example.

It is another object to provide a heat-exchange device configured tooperate in a fluid medium, said heat-exchange device comprising aplurality of heat-exchange elements arranged in a three-dimensionalspace in a first fractal configuration, each respective heat-exchangeelement being perforated with a plurality of holes to allow the fluidmedium to flow through the holes, the plurality of holes being arrangedaccording to a second fractal pattern. The plurality of holes arearranged in a pattern corresponding to

-   -   an Appolony Fractal (paulbourke.net/fractals/apollony/,        paulbourke.net/papers/apollony/apollony.pdf),    -   a Circle Inversion Fractal        (en.wikipedia.org/wiki/List_of_mathematical_shapes),    -   a Circle Packing Fractal        (en.wikibooks.org/wiki/Fractals/Apollonian_fractals),    -   Apollonian Gasket (en.wikipedia.org/wiki/Apollonian_gasket),    -   a Sierpinski Carpet, and    -   a Hex Fractal Carpet        (erkdemon.blogspot.com/2009/12/hex-fractal-carpet.html,        www.nahee.com/spanky/www/fractint/lsys/truefractal.html).

It is a further object to provide an electronic device having at leastone electronic component generating excess heat and a heat-exchangedevice coupled to said electronic component to dissipate heat from theelectronic component, said heat-exchange device comprising a pluralityof heat-exchange elements arranged in a three-dimensional space in afirst fractal configuration, each respective heat-exchange elementhaving a surface texture arranged in a second fractal configuration.

It is a still further object to provide an electronic device having atleast one electronic component generating excess heat and aheat-exchange device coupled to said electronic component and configuredto operate in a fluid medium, to dissipate heat from the electroniccomponent, said heat-exchange device comprising a plurality ofheat-exchange elements arranged in a three-dimensional space in a firstfractal configuration, each respective heat-exchange element beingperforated with a plurality of holes arranged according to a secondfractal pattern, configured to allow the fluid medium to flow throughthe holes.

It is another object to provide a method of operating an electronicdevice having at least one electronic component generating excess heat,the method comprising the steps of: conducting the heat away from saidat least one electronic component generating excess heat to theheat-exchange device coupled to said at least one electronic component,said heat-exchange device comprising a plurality of heat-exchangeelements arranged in a three-dimensional space in a first fractalconfiguration, each said heat-exchange element having a surface texturearranged in a second fractal configuration; and dissipating the excessheat from the heat-exchange elements into the environment.

Another object provides a method of operating an electronic devicehaving at least one electronic component generating excess heat, themethod comprising the steps of: conducting the heat away from said atleast one electronic component generating excess heat to theheat-exchange device coupled to said at least one electronic componentand configured to operate in a fluid medium, said heat-exchange devicecomprising a plurality of heat-exchange elements arranged in athree-dimensional space in a first fractal configuration, eachrespective heat-exchange element being perforated with a plurality ofholes arranged according to a second fractal pattern configured to allowthe fluid medium to flow through the holes; and dissipating the excessheat from the heat-exchange elements into the fluid medium.

It is a still further object to provide a method of dissipating heat,comprising: providing a heat transmissive body, having a base configuredto receive a heat load, and a three dimensional configuration having anexternal surface configured to transfer a heat load corresponding to theheat load received by the base to an external heat transfer fluid;interacting a multiscale pattern associated with the external surfacewith a flow of the external heat transfer fluid, to generate turbulencein the a flow of the external heat transfer fluid and reduce a stagnantsurface layer to facilitate heat transfer; and controlling the flow ofthe external heat transfer fluid based on at least one measurementcorresponding to at least one of a heat transfer of the heat load to theexternal heat transfer fluid and a turbulence of the flow of theexternal heat transfer fluid. The controlling may be dependent on anacoustic emission, a correspondence of a temperature of the heattransmissive body to a computation flow dynamics model of heat transferin the heat transmissive body, a thermodynamic parameter. The controlcan alter turbulence, and in particular may control the onset oroccurrence of significant turbulence, the location of turbulence, andamount of turbulence, for example. On the other hand, the control canseek to avoid turbulence, and modify flow parameters to meet thermalcriteria while avoiding objectionable noise. The control can alsodynamically change turbulence, for example as a way to createconcentrated surface forces as a way to dislodge particles on thesurface of the heat sink. Further, by dynamically controllingturbulence, heat dissipation may be selectively increased in variousregions of the heat sink at different times. The dynamic process maytherefore locally reduce air flow to permit an increase in temperature,and then selectively increase the air flow, providing high efficiencyheat dissipation due to the combination of higher temperaturedifferential and reduced boundary layer thickness. This dynamic processmay have a higher efficiency than a static process wherein thetemperature differential between the heat sink surface and the heattransfer medium is stabilized at a low difference, and a uniform,distributed air flow leads to a uniformly relatively thicker boundarylayer.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a fractal heat sink that is an exemplary embodimentof the invention, in which the heat sink is based on a Quadratic KochIsland, or a fractal flow filter.

FIGS. 2A-2C illustrate the basis for the Quadratic Koch Island, aQuadratic Koch Island obtained after application of one iteration, and aQuadratic Koch Island obtained after application of several iterations.

FIG. 3 illustrates the total length of all the fractal segments of aQuadratic Koch Island.

FIGS. 4A and 4B illustrate a basis for generating the modifiedSnowflake, and the modified Koch Snowflake.

FIGS. 5A and 5B illustrates a fractal heat sink that based on aSierpinski Carpet, and the basis for generating the Sierpinski Carpet.

FIGS. 6-15 illustrate fractal heat sinks that based on athree-dimensional Mandelbox fractal, a Sierpinski tetrahedron, aDodecaedron fractal, an Icosahedron flake, an Octahedron flake, a 3DQuadratic Koch, a Jerusalem cube, a von Koch surface, a Menger sponge,and a 3D H fractal, respectively.

FIGS. 16-17 show a face and perspective view of a prior art extrudedheat sink having an irregular design.

FIG. 18 shows the design according to FIGS. 16 and 17 with a fractalsurface pattern.

FIGS. 19-21 illustrate various three-dimensional fractal-likestructures, which may be used to induce turbulence in a flowing heattransfer medium, or may act as heat sinks for a heat source, which maybe located centrally or eccentrically within the respective structure.

FIG. 22 shows a branching array of elements, which have increasingsurface area:cross section area with increasing distance from the root.A multiscale pattern (not shown) may be formed on the surfaces.

FIG. 23 shows a solid fractal mass with based on Serpinski's trangles,with a set of exposed surfaces.

FIG. 24 shows a prior art heat sink for a lamp;

FIGS. 25-26 show a top view of heat sink simulation models correspondingto the prior art heat sink shown in FIG. 24 , with different number ofbranches, and the approximately calculated thermal resistance trend forone branch and simulation results of the same branch of a branched heatsink.

FIGS. 27-28 shows simulation results of normalized thermal resistancefor different numbers of branches, and a cross section view of a thermalmodel showing internal temperature and external air velocity for a plateand branched heat sink.

FIG. 29 shows a radially symmetric branched heat sink, with two levelsof branching.

FIG. 30 shows an incremental range of cross sections for heat sinks,with increasing heat transfer coefficient toward the right.

FIGS. 31 and 32 show a radially symmetric heat sink with a progressiveincrease in the number of plate surfaces with increasing distance fromthe center (FIG. 31 ), or a branching pattern (FIG. 32 ), each platehaving a superimposed fractal pattern in the form of a texture.

FIG. 33 shows a heating comprising a regular array of radiator elements,each element being textured with a fractal surface pattern to increaseheart transfer.

FIG. 34 shows a Koch snowflake external pattern with a perforatedinternal pattern.

FIGS. 35-37 show branched network fractal grid, of a first type, asecond type with 4 orders of elements, and a third type with 5 orders ofelements, respectively.

FIGS. 38-40 show a branched network heat sink with a fractal perforationpattern and first and second detail of the pattern, respectively.

FIG. 41 shows a detail of a first serpentine microchannel pattern withinthe heat sink plates of FIG. 38 .

FIG. 42 shows a detail of a second serpentine microchannel patternwithin the heat sink plates of FIG. 38 .

FIG. 43 shows a detail of a first branched microchannel pattern withinthe heat sink plates of FIG. 38 .

FIG. 44 shows a detail of a second branched microchannel pattern withinthe heat sink plates of FIG. 38 .

FIG. 45 shows a detail of a textured surface of the heat sink plates ofFIG. 38 .

FIG. 46 shows a top perspective view of hollow conical perforatedstructure heat sink having a set of fractal branched fins extendingradially.

FIG. 47 shows a side perspective view of the heat sink according to FIG.46 .

FIG. 48 shows the hollow frustum of the conical perforated structureheat sink shown in FIG. 46 , absent the set of branched fins.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 illustrates a fractal heat sink that is an exemplary embodimentof the invention. In this embodiment, the heat sink is based on aQuadratic Koch Island. In a shorter length, this also represents afractal flow filter. The Quadratic Koch Island may have a regular orirregular twist pattern within the shroud.

FIG. 2A illustrates the basis for the Quadratic Koch Island.

FIG. 2B illustrates a Quadratic Koch Island obtained after applicationof one iteration.

FIG. 2C illustrates a Quadratic Koch Island obtained after applicationof several iterations. FIG. 3 illustrates the total length of all thefractal segments of a Quadratic Koch Island.

FIG. 2A illustrates a square with dimension x₀ that forms the basis forthe Quadratic Koch Island.

FIG. 2B illustrates a Quadratic Koch Island obtained after applicationof one fractal iteration on the square. The fractal with section lengthsof l is applied to each side of the square in the first iteration.Similarly, after several such iterations, a Quadratic Koch Island asillustrated in FIG. 2C may be obtained.

FIG. 3 illustrates the length of the fractal l_(f) which is the totallength of all the fractal segments. The length of each fractal section,l(n), decreases with each iteration of the fractal. The fractal sectionlength is described by eq. 7.

$\begin{matrix}{{l(n)} = {\left( \frac{1}{4} \right)^{n}x_{0}}} & (7)\end{matrix}$

where, x₀ is the length of the side of the original square, n is thenumber of iterations, and A_(s), the surface area, can be seen from eq.7, the fractal section length decreases after each iteration. When thenumber of iterations becomes increasingly large, the section lengthtends towards being negligible.

Further, it may be mathematically shown that the overall length L of thefractal may be obtained from eq. 8.

$\begin{matrix}{{L(n)} = {x_{0}\left( {1 + {\frac{2}{3}\left( {1 - \frac{1}{4^{n}}} \right)}} \right)}} & (8)\end{matrix}$where, x₀ is the length of the side of the original square and n is thenumber of iterations.

Similarly, it may be shown that the circumference C of the QuadraticKoch Island can be obtained from eq. 9.C=4(2^(n) x ₀)  (9)where, x₀ is the length of the side of the original square and n is thenumber of iterations. It is evident that with each iteration, thecircumference C increases. However, the cross-sectional area remainsconstant at x₀ ²; since when a fractal area is added the same area issubtracted elsewhere.

The number of iterations corresponding to the Quadratic Koch Island maybe greater than 5. Consequently, the heat exchange device functions as acompact heat exchanger. In other words, the heat exchange device has alarge heat transfer area per unit exchanger volume. As a result, severaladvantages are obtained such as, but not limited to, reduction in space,weight, power requirements and costs. In another embodiment, the numberof iterations corresponding to the Quadratic Koch Island may be lessthan or equal to 5. Consequently, the heat exchange device may functionas a non-compact heat exchanger. The Quadratic Koch Island extended inthe third dimension, as shown in FIG. 1 , so that the cross-sectionremains a two-dimensional Quadratic Koch Island.

It may be shown with heat transfer analysis that heat transfer and heattransfer coefficient increase independently of each other with everyapplication of the fractal. Further, the increase may be double, orgreater, with every fractal iteration. In general, the increase in heattransfer is exponential following a trend of 2^(n). Moreover, pumpingpower increases linearly, at almost one and a half the rate. Pumpingpower is the power needed to pump the heat transfer fluid through theheat exchange device.

FIG. 4A illustrates a basis for generating a modified Snowflake.

FIG. 4B illustrates a fractal heat sink based on the modified KochSnowflake of FIG. 4A, which has triangles of different scales. Thisdesign can be extended into three dimensions, as shown in FIGS. 11 and23 , which build upon pyramids.

The basis for generating the modified Snowflake is an equilateraltriangle of width w, as illustrated in FIG. 4A. In the first iteration,two smaller equilateral triangles of width ⅓ of the base width w areadded onto two sides of the base triangle. Similarly, by applying secondand a third iteration, the modified Koch Snowflakes as illustrated inFIG. 4B may be obtained.

In general, for a self-similar object that can be decomposed into mself-similar elements with a magnification factor n, the fractaldimension is given by:

$D = {\frac{\log m}{\log n} = \frac{{{lo}g}\left( {{{number}{of}{self}}‐{{similar}{elements}}} \right)}{\log\left( {{magnification}{factor}} \right)}}$

The fractal dimension of the Koch snowflake is given by

$D = {\frac{\log 4}{\log 3} \simeq {{1.2}6186}}$

The surface area, A_(s)(n), of the modified Koch Snowflake (includingsidewalls) may be obtained from eq. 10.

$\begin{matrix}{{A_{s}(n)} = {{2\left( {{wt} + {\frac{\sqrt{3}}{4}w^{2}}} \right)} + {\sum_{1}^{n}{\left\lbrack {{\left( \frac{w}{3^{n}} \right)^{2}\left( \frac{\sqrt{3}}{2} \right)} + {\left( \frac{w}{3^{n}} \right)t}} \right\rbrack 2^{{2n} - 1}}}}} & (10)\end{matrix}$

where, w is the width of the base triangle, n is the number ofiterations, and t is the thickness of the modified Koch Snowflake (notlabelled in FIG. 4B).

It is evident that the surface area of the modified Koch Snowflakeincreases with each iteration. More specifically, it may be observedthat after 5 iterations there is an increase in surface area of about58%.

Further, the mass of the modified Koch Snowflake may be obtained usingeq. 11.

$\begin{matrix}{{m(n)} = {\left\{ {{\frac{\sqrt{3}}{4}w^{2}} + {\sum_{1}^{n}{\left\lbrack {\left( \frac{w}{3^{n}} \right)^{2}\left( \frac{\sqrt{3}}{4} \right)} \right\rbrack 2^{{2\pi} - 1}}}} \right\}\rho t}} & (11)\end{matrix}$

where, w, n, and t are as above, and ρ is the density of the materialmaking up the modified Koch Snowflake.

It may be observed that the change in surface area with respect to thebaseline case (i.e., n=0) is a function of width (w) and thickness (t).However, the change in mass with respect to the baseline is dependent onthe number of iterations. The mass of a design according to the modifiedKoch Snowflake increases with each iteration. However, it converges to amaximum value of mass increase of approximately 40%.

A heat transfer effectiveness (ε) of a heat exchanger made approximatelyin a shape of the modified Koch Snowflake may be defined as the ratio ofheat transfer achieved to heat transfer that would occur if the modifiedKoch Snowflake was not present. E may be calculated from eq. 12.

$\begin{matrix}{\varepsilon = \frac{Q_{c}}{h{A_{s}\left( {T_{b} - T_{\infty}} \right)}}} & (12)\end{matrix}$

where, Q is the heat rate, h is the heat transfer coefficient, A_(s) isthe area, and Tis the temperature.

Further, a heat-transfer efficiency (η) of a heat exchanger madeapproximately in a shape of the modified Koch Snowflake may be definedas the ratio of heat transfer achieved to the heat transfer that wouldoccur if the entire modified Koch Snowflake was at the base temperature.η may be calculated from eq. 13, where, Q, h, As, and T are as above.

$\begin{matrix}{\eta = \frac{Q_{c}}{h{A_{s}\left( {T_{b} - T_{\infty}} \right)}}} & (13)\end{matrix}$

The heat transfer effectiveness (ε) increases with each iteration. Themodified Koch Snowflake corresponding to three iterations may be used toform the heat exchange device. Accordingly, the heat transfereffectiveness (ε) may increase by up to 44.8%. Further, the increase inheat transfer effectiveness (ε) per mass may be up to 6%. The materialused to make the modified Koch Snowflake may be aluminum. Consequently,heat transfer effectiveness (6) per mass of approximately two timeslarger than that obtained using copper may be achieved.

Further, the heat transfer effectiveness (ε) per mass depends on thethickness the heat-exchange plate with a shape of the modified KochSnowflake. The ratio of width (w) to thickness (t) corresponding to themodified Koch Snowflake may be 8. Accordingly, an increase in heattransfer effectiveness (ε) per mass of up to 303% may be achieved at thefourth iteration.

FIG. 5A illustrates a fractal heat sink that is based on a SierpinskiCarpet.

FIG. 5B illustrates the basis for generating the Sierpinski Carpet. TheSierpinski Carpet is formed by iteratively removing material from a basegeometry such as, but not limited to, a square as illustrated in FIG.5B. In the first iteration, a square with ⅓ of the base width (w) isremoved. Similarly, by performing second and third iterations, theSierpinski Carpets as illustrated in FIG. 5A may be obtained.

The surface area, A_(s)(n), of the Sierpinski Carpet (includingsidewalls) may be obtained from eq. 14.

$\begin{matrix}{{A_{s}(n)} = {{2w^{2}} + {3wt} - {\sum_{1}^{n}{8^{n - 1}\left\lbrack {{2\left( \frac{w}{3^{n}} \right)^{2}} - {4\left( \frac{w}{3^{n}} \right)t}} \right\rbrack}}}} & (14)\end{matrix}$

where, w is the width of the base square, n is the number of iterations,and t is the thickness of the Sierpinski Carpet.

Starting from n=0, with each subsequent iteration, the surface area ofthe Sierpinski carpet initially reduces before reaching a minimum.However, after reaching the minimum, the surface area increases witheach subsequent iteration. For example, at a width (w) of 0.0508 m anincrease in surface area of 117% may be obtained after five iterations.Similarly, at a width (w) of 0.0254 m, a surface area increase of 265%may be obtained after five iterations.

Further, the mass of the Sierpinski Carpet may be obtained using eq. 15.

$\begin{matrix}{{m(n)} = {\left\{ {w^{2} - {\sum_{1}^{n}\left\lbrack {8^{n - 1}\left( \frac{w}{3^{n}} \right)^{2}} \right\rbrack}} \right\}\rho t}} & (15)\end{matrix}$

where w, n, and t are as above, and ρ is the density of the materialmaking up the Sierpinski carpet.

It may be seen from eq. 15 that with each iteration, the mass of theSierpinski carpet decreases. For example, after five iterations, thereis a 45% mass reduction.

The heat transfer effectiveness (ε) corresponding to the Sierpinskicarpet increases with each iteration. The Sierpinski carpetcorresponding to three iterations may be used to form the heat exchangedevice. Accordingly, in this case, the heat transfer effectiveness (ε)may increase by up to 11.4%. Further, the increase in heat transfereffectiveness (ε) per mass corresponding to the Sierpinski carpet may beup to 59%. The material used to make the Sierpinski carpet may bealuminum. Consequently, heat transfer effectiveness (ε) per mass ofapproximately two times larger than that obtained using copper may beachieved.

Further, the heat transfer effectiveness (ε) per mass corresponding tothe Sierpinski carpet depends on the thickness of the corresponding tothe Sierpinski carpet. The ratio of width (w) to thickness (t)corresponding to the Sierpinski carpet may be 8. Accordingly, a 303%increase in heat transfer effectiveness (ε) per mass may be achieved atthe fourth iteration.

The heat sink may also comprise a heat exchange device which isstructurally configured based on, but not limited to, one or morefractals selected from the group comprising: A “scale 2” and “scale 3”Mandelbox; Sierpinski tetrahedron; Fractal pyramid; Dodecahedronfractal; 3D quadratic Koch surface (type 1); 3D quadratic Koch surface(type 2); Jerusalem cube; Icosahedron fractal; Octahedron fractal; VonKoch surface; Menger sponge; 3D H-fractal; Mandelbulb; or any number ofother 2D and 3D fractals and combinations thereof. 2D and 3D, as usedherein, mean topologically two-dimensional and three-dimensional objectsrespectively.

FIG. 6 illustrates a fractal heat sink that is based on athree-dimensional Mandelbox fractal. In practice, the Mandelbox does notneed to be complete, and may be cut to provide a suitable interface to aheat source. A Mandelbox is a box-like fractal object that has similarproperties as that of the Mandelbrot set. It may be considered as a mapof continuous, locally shape preserving Julia sets. Accordingly, theMandelbox varies at different locations, since each area uses a Juliaset fractal with a unique formula. The Mandelbox may be obtained byapplying eq. 16 repeatedly to every point in space. That point v is partof the Mandelbox if it does not escape to infinity.v=s*ballFold(r,f*boxFold(v))+c  (16)

where boxFold(v) means for each axis a:

-   -   if v[a]>1 v[a]=2−v[a], else if v[a]<−1 v[a]=−2−v[a]

and ballFold(r, v) means for v's magnitude m:

-   -   if m<r m=m/r², else if m<1 m=1/m

In an instance, using the values of s=2, r=0.5 and f=1 in eq. 12, thestandard Mandelbox may be obtained.

Because the Mandelbox is inherently a three-dimensional shape, it may beused in conjunction with a multiscale filter, such as a fractal grid orthe device according to FIG. 15 , to induce turbulent flows in the heatexchange fluid surrounding the Mandelbox. It is noted that the Mandexboxis a case where the surface texture and the morphology are defined by asingle generative algorithm, and therefore the structure inherentlypossesses similarities in terms of fluid dynamical performance withother designs according to the present invention that employ distinctgenerative algorithms. A formal Mandelbox is difficult to manufacture,and optimizing internal configuration of a complete Mandelbox is alsosomewhat challenging. Therefore, the Mandelbox approach may beimplemented as a surface configuration of a solid heat sink, to providemultiscale surface features while providing a dense core structure.

FIG. 7 illustrates a fractal heat sink that is based on a Sierpinskitetrahedron, over a range of orders. The Sierpinski tetrahedron, alsocalled as tetrix, is a three-dimensional analogue of the Sierpinskitriangle. The Sierpinski tetrahedron may be formed by repeatedlyshrinking a regular tetrahedron to one half its original height, puttingtogether four copies of this tetrahedron with corners touching, and thenrepeating the process. This is illustrated in FIG. 7 for the first fouriterations. The Sierpinski tetrahedron constructed from an initialtetrahedron of side-length L has the property that the total surfacearea remains constant with each iteration.

The initial surface area of the (iteration-0) tetrahedron of side-lengthL is L²√3. At the next iteration, the side-length is halved and thereare 4 such smaller tetrahedra. Therefore, the total surface area afterthe first iteration may be calculated by eq. 17.

$\begin{matrix}{4{\left( {\left( \frac{L}{2} \right)^{2}\sqrt{3}} \right) = {{4\frac{L^{2}}{4}\sqrt{3}} = {L^{2}\sqrt{3}}}}} & (17)\end{matrix}$

This remains the case after each iteration. Though the surface area ofeach subsequent tetrahedron is ¼ that of the tetrahedron in the previousiteration, there are 4 times as many—thus maintaining a constant totalsurface area. However, the total enclosed volume of the Sierpinskitetrahedron decreases geometrically, with a factor of 0.5, with eachiteration and asymptotically approaches 0 as the number of iterationsincreases.

FIG. 8 illustrates a fractal heat sink that is based on a Dodecaedronfractal, also called a dodecahedron flake, which may be formed bysuccessive flakes of twenty regular dodecahedrons, as exemplarilyillustrated in FIG. 8 for a second iteration. Each flake is formed byplacing a dodecahedron scaled by 1/(2+φ) in each corner, whereinφ=(1+√5)/2.

FIG. 9 illustrates a fractal heat sink that is based on an Icosahedronflake, showing octahedron flake, or Sierpinski octahedron, which may beformed by successive flakes of six regular octahedrons, as exemplarilyillustrated in FIG. 9 for a third iteration. Each flake may be formed byplacing an octahedron scaled by ½ in each corner. Each flake may beformed by placing an icosahedron scaled by 1/(2+φ) in each corner,wherein φ=(1+√5)/2.

FIG. 10 illustrates a fractal heat sink that is based on an Octahedronflake. The heat absorption surface may be any face of the Octahedronflake, or the flake may be bisected and the resulting semi-Octahedronflake mounted to a surface for heat dissipation.

FIG. 11 illustrates a fractal heat sink that is based on a 3D QuadraticKoch. As exemplified in FIG. 11 , the 3D Quadratic Koch may be obtainedby growing a scaled down version of a triangular pyramid onto the facesof the larger triangular pyramid with each iteration. FIG. 11illustrates the first four iterations.

FIG. 12 illustrates a fractal heat sink that is based on a Jerusalemcube. The Jerusalem cube may be obtained by recursively drilling Greekcross-shaped holes into a cube. The Jerusalem Cube may be constructed asfollows: (1) Start with a cube; (2) Cut a cross through each side of thecube, leaving eight cubes (of rank+1) at the corners of the originalcube, as well as twelve smaller cubes (of rank+2) centered on the edgesof the original cube between cubes of rank+1; and (3) Repeat the processon the cubes of rank 1 and 2. Each iteration adds eight cubes of rankone and twelve cubes of rank two, a twenty-fold increase.

FIG. 13 illustrates a fractal heat sink that is based on a von Kochsurface. The von Koch surface may be constructed by starting from anequilateral triangular surface. In the first iteration, the midpoints ofeach side of the equilateral triangular surface are joined together toform an equilateral triangular base of a hollow triangular pyramid. Thisprocess is repeated with each iteration.

FIG. 14 illustrates a fractal heat sink that is based on a Mengersponge. The Menger sponge may be constructed as follows: (1) Begin witha cube (first image); (2) Divide every face of the cube into 9 squares,like a Rubik's Cube. This will sub-divide the cube into 27 smallercubes; (3) Remove the smaller cube in the middle of each face, andremove the smaller cube in the very center of the larger cube, leaving20 smaller cubes (second image). This is a level-1 Menger sponge(resembling a Void Cube); and (4) Repeat steps 2 and 3 for each of theremaining smaller cubes, and continue to iterate until a desired scaleis reached.

FIG. 15 illustrates a fractal heat sink that is based on a 3D H fractal.As noted above, according to some embodiments, this structure is used toinduce turbulent flow, and it not itself a heat sink; in otherembodiments, the 3D frame is both a turbulence generating structure anda heat sink. The 3D H fractal is based on an H-tree which may beconstructed by starting with a line segment of arbitrary length, drawingtwo shorter segments at right angles to the first through its endpoints,and continuing in the same vein, reducing (dividing) the length of theline segments drawn at each stage by √2. Further, by adding linesegments on the direction perpendicular to the H tree plane, the 3D Hfractal may be obtained.

The heat sink may comprise a heat exchange device which is structurallyconfigured based on a Mandelbulb (not shown). The Mandelbulb is athree-dimensional analogue of the Mandelbrot set. The Mandelbulb may bedefined as the set of those C in

³ for which the orbit of <0, 0, 0> under the iteration v|−→v^(n)+c isbounded, where the “nth power” of the vector v=

x, y,

in

³ is given by eq. 17.v ^(n) :=r ^(n)

sin(nθ)cos(nϕ,sin(nθ)sin(nϕ),cos(nθ)

  (17)

Where

r=√{square root over (x²+y²+z²)},

ϕ=arctan(y/x)=arg(x+yi), and

θ=arctan(√{square root over (x²+y²)}/z)=arccos(z/r).

As with the Mandelbox, the surface texture and the morphology of theSierpinski tetrahedron, Dodecaedron fractal, Icosahedron flake,Octahedron flake, 3D Quadratic Koch, Jerusalem cube, von Koch surface,Menger sponge, 3D H fractal, and Mandelbulb structures are each definedby a single generative algorithm. The 3D fractal (multiscale) structuremay be coupled in use with an external multiscale element (or the sameor a different multiscale 2D or 3D structure) which interacts with theheat transfer fluid to induce turbulent flows, or may be provided as asurface configuration of an independently defined heat sink morphology.For example, a 3D multiscale structure may be self-organizing on asurface, provided as a section of a formal shape, or the designprinciples used to generate the morphology using the basic surfaceconfiguration and other mechanical limits as constraints in thegenerative algorithm.

FIGS. 16-17 show a face and perspective view of a prior art extrudedheat sink having an irregular design.

FIG. 18 shows the design according to FIGS. 16 and 17 with a fractalsurface pattern. In similar manner, the present technology permits heatexchange surfaces to be modified with a surface texture or perforationpatterns that interact with heat exchange fluid flows, and over a rangeof flows, induce turbulence.

FIGS. 19-21 illustrate various three dimensional fractal-likestructures, which may be used to induce turbulence in a flowing heattransfer medium, or may act as heat sinks for a heat source, which maybe located centrally or eccentrically within the respective structure.

FIG. 22 shows a branching array of elements, which have increasingsurface area:cross section area with increasing distance from the root.A multiscale pattern (not shown) may be formed on the surfaces. Asdiscussed above, the structure may have vibrations, especially underturbulent flow conditions, which can increase heat dissipationefficiency.

FIG. 23 shows a solid fractal mass with based on Sierpinski's triangles,with a set of exposed surfaces.

A Computational Flow Dynamics (CFD) model is a mathematical approachwhich may be used to estimate the thermal resistance of naturallybranched structures. A prior art CFD implementation is based to theassumption of the steady state and considers the energy loss in thebranch by heat conduction and heat convection. The bifurcations aremodeled by a recursive rule to calculate the thermal resistance of thewhole branch. Input parameters are geometric properties of every singlesector of the branch including its length, width and height, the thermalconductivity of the material and the heat transfer coefficient on thesurfaces. This coefficient takes account of the geometry of the heatsink because it respects the flow conditions round the surfaces that areinfluenced by the space available for air flow. In the CFD model, withan increasing number of bifurcations, thermal resistance initiallydecreases. After reaching its minimum value it increases again. Thiseffect is caused by a change in convective heat dissipation with thelength of the branched sectors.

In the prior art design, assuming constant total length and materialvolume of the branch, the surface for convection is increased with everynew bifurcation. At the same time, each new sector reduces the spacebetween the neighbor branches and affects the airflow between thesurfaces negatively. At a specific number of bifurcations the reducedairflow no longer compensates the benefit from the newly generatedsurfaces. In consequence, the thermal resistance rises. If the spacingbetween the surfaces is too small, the fluid-flow through the channelsis hindered and the heat transport by convection is reduced.

FIG. 24 shows a stylized radially symmetric branched heat sink designedaccording to this method. According to the present technology, theexposed surfaces of the heat sink are further textured, such as byetching, additive manufacturing, laser processing, or other knownprocessing schemes, to assume a fractal surface configuration,superimposed on the underlying branched network. See, A. Sachs, B.Bergdoll, D. Gamboni and P. Ursprung: Nature Design. Museum fürGestaltung Zurich, Lars Müller Publishers, Zürich 2007; C. Herbold andC. Neumann: Vorbild Natur: Bionische Strukturen zur Entwärmung von LEDs.Tagungsband LICHT, Berlin 2012; A. Bar-Cohen and W. M. Rohsenow:Thermally Optimum Spacing of Vertical, Natural Convection Cooled,Parallel Plates, J. Heat Transfer, 106, pp. 116-123, 1984; A. Bejan andS. Lorente: Design with Construcal Theory. John Wiley & Sons, Inc.,Hoboken, N.J. 2008; MIM-Expert-Group and Fraunhofer-IFAM: MetalInjection Moulding (MIM), Powder Injection Moulding, 2012. As with other3D designs, the structure may be modified according to the presenttechnology to include a surface pattern or perforation pattern which hasmultiscale characteristics, or used in conjunction with another separatemultiscale element to improve performance.

The branches of this prior art design are constructed in one plane thatis extended in the third dimension to form a cylindrical body. Thiscylinder has a diameter of 50 mm and a height of 50 mm. All simulationsare performed with a thermal power dissipation of 7 W on an area of 5mm×5 mm in the middle of the bottom end plane, with passive flow of theheat transfer medium.

FIG. 26 shows the approximately calculated trend of thermal resistancefor one branch (grey) and simulation results of the same branch (black).Based on the results of the CFD mathematical approximation, differentparameters of the geometry are evaluated in detail by thermalsimulations.

According to the present technology, the branches may be asymmetric, andthe branches may be non-constant length, and therefore, while a limitmay still be reached as to the increasing marginal utility of branches,that limit may be increased, or increased efficiency achieved with thesame mass or operating cost. Further, by addressing surfaceconfiguration rather than gross morphology only, the heat transfercoefficient of the heat sink is increased, and flow restriction can bedecreased.

The prior art heat sinks in FIG. 25 shows a top view of heat sinksimulation models with different number of branches. The models containfive to nine branches with two symmetric bifurcations in every branch.Simulation results show that the lowest thermal resistance of thesedesigns is achieved with seven branches where the difference is up to12%. The low number of branches in heat sinks 1 and 2 wastes space foradditional surfaces while the large surfaces of heat sinks 4 and 5 causenarrow flow channels between the branches.

FIG. 27 shows simulation results for the different numbers of branches.

FIG. 28 shows the temperature distribution on the surface of both typesas well as the flow velocity in the center plane. The highertemperatures and the areas with low flow velocity at the branched heatsink are obvious. The thermal resistance of the non-branched heat sinkis 8.3% higher compared to the thermal resistance resulting for thebranched version.

FIG. 29 shows a stylized radially symmetric branched heat sink, with twolevels of branching. The surfaces of this heat sink may be perforated orpatterned as described herein.

FIG. 30 shows an incremental range of cross sections for extruded heatsinks, with increasing passive heat transfer coefficient toward theright. Note that actual heat transfer depends on heat transfer fluidcharacteristics, and passive convection or laminar may not apply,especially where turbulence is intentionally introduced in the medium.However, by providing a heat sink design that has reasonable performanceunder laminar flow or passive convective cooling conditions, a mode ofoperation is provided which is tolerant of fan failure, and permitsreduced fan energy consumption and acoustic emissions. The optimizationof the algorithm may therefore take into account not only peak heatdissipation capability, but also performance under low heat load,jointly optimizing both ranges of operation.

FIGS. 31 and 32 show a radially symmetric heat sink with a progressiveincrease in the number of plate surfaces with increasing distance fromthe center (FIG. 31 ), or a branching pattern (FIG. 32 ), each platehaving a superimposed fractal pattern in the form of a texture.

FIG. 33 shows a heating comprising a regular array of radiator elements,each element being textured with a fractal surface pattern to increaseheart transfer. These textured surfaces will induce vorticescharacteristic of turbulence near the surface under certain flowconditions, and for a given flow rate, increase heat dissipationcapacity.

According to one embodiment the present technology, the pattern on eachaxis would general demonstrate its own self-similar configuration, andthe patterns would not be overlaid on orthogonal axes, resulting ininterscale interactions.

FIG. 34 shows a Koch snowflake external pattern with a perforatedinternal pattern. This may be used as a fractal grid or as a surfacepattern of a heat exchange surface.

FIG. 35 shows a first type of branched network fractal grid.

FIG. 36 shows a second type of branched network fractal grid, with 4orders of elements.

FIG. 37 shows a third type of branched network fractal grid, similar toFIG. 36 , but with 5 orders of elements. These are known for use asfractal grids for inducing air flow turbulence.

FIG. 38 shows an exemplary branched network heat sink, with a fractalperforation pattern.

FIG. 39 shows a first detail of the perforation pattern of FIG. 38 .

FIG. 40 shows a second detail of the perforation pattern of FIG. 38 . Inaccordance with as perforated surface embodiment of the inventiondisclosed herein, the heat sink comprises a heat exchange device havingheat exchange surfaces which are perforated. As a result, enhanced heattransfer may be achieved. Additionally, use of perforations may increaseheat transfer by up to a factor of two per pumping power. Further, theplurality of heat exchange elements may be hollow. The combination ofhollow heat exchange elements with perforations can result in increasesin heat transfer greater than that of a solid heat exchange element ofthe same diameter. Additionally, increases in heat transfer per pumpingpower of up to 20% could be achieved by varying the inclination angleand diameter of the perforations in aligned arrays of the plurality ofheat exchange elements. Furthermore, one or more of the number ofperforations and shape of perforations may be configured in order tocontrol the heat transfer. For instance, under natural convection, heattransfer is directly proportional to the number of square perforations.In another instance, circular and square perforations may be used toobtain higher Nusselt number. Since heat transfer is proportional toNusselt number, greater heat transfer may be achieved with such anarrangement. In yet another instance, the Nusselt number correspondingto the plurality of heat exchange elements may be varied based on one ormore of a pitch, a hole diameter, a surface area and flow velocity. Inparticular, by modifying the pitch of the perforations, the Nusseltnumber and hence heat transfer may be increased.

FIG. 41 shows a detail of a first serpentine microchannel pattern withinthe heat sink plates of FIG. 38 .

FIG. 42 shows a detail of a second serpentine microchannel patternwithin the heat sink plates of FIG. 38 .

FIG. 43 shows a detail of a first branched microchannel pattern withinthe heat sink plates of FIG. 38 .

FIG. 44 shows a detail of a second branched microchannel pattern withinthe heat sink plates of FIG. 38 .

Microchannel heat sink technology, both serpentine and branched channel,have been previously studied. The present technology enhances suchdesigns by permitting 3D designs, rather that the available planarconfigurations, and can combine both internal fluid flows with externalheat transfer medium flows, which can be jointly optimized, to improveperformance. In some cases, a compressed gas is fed to into themicrochannel, which is then released at strategic locations, to induceturbulent flows on external cooling surfaces of the device.

FIG. 45 shows a detail of a textured surface of the heat sink plates ofFIG. 38 .

A list of common fractals, with their exact and calculated Hausdorffdimension, fromen.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension, isprovided in Table 1. See also en.wikipedia.org/wiki/Fractal_dimension.

The surfaces of the heat exchange surfaces may have a texture, which isspatially optimized according an independent fractal algorithm. Where anadditive or subtractive manufacturing process is employed, the surfaceconfiguration may be according to a fractal algorithmic design. Thesurface of triangles may include holes arranged in a fractal pattern, orit may include etching or channels for cooling liquid branchingaccording to a fractal algorithm. In other cases, the surfaceconfiguration may be determined by a self-organizing or self-assemblingcoating. The coating may have characteristics that vary over space,which may be dependent on a curing temperature, and thus, if the heatsource is the solid to be cooled and a representative air flow patternduring cooling, the texture will be dependent on the low-levelmorphology and heat sink design. The coating may also be induced tospatial variation through other physical means, such as aphotolithographic curing of a texturing material, or other manufacturingtechniques.

The fractal shape may have some apertures in it (not illustrated) toallow the solid to be cooled to connect with other elements. The solidshould be connected to the fractal heat sink through an efficient heatconduction surface.

A spacing between the plurality of heat exchange elements is determinedbased on a height of the plurality of heat exchange elements. For agiven heat rate, an optimal spacing between the plurality of heatexchange elements may decrease with an increase in height of theplurality of heat exchange elements.

A shape corresponding to the plurality of heat exchange elements may beconfigured to provide enhanced heat transfer. For instance, theplurality of heat exchange elements may be fluted. In another instance,the plurality of heat exchange elements may be wavy. The shapecorresponding to the plurality of heat exchange elements may betriangular, circular, elliptical, rectangular and trapezoidal. Forinstance, the plurality of heat exchange elements may be ellipticallyannular. Further, an elliptical aspect ratio corresponding to theplurality of heat exchange elements may be varied in order to obtaingreater heat transfer efficiency. As a non-limiting example, theelliptical aspect ratio may be increased in order to obtain higher heattransfer efficiency. In another instance, the plurality of heat exchangeelements may be trapezoidal with an optimal aspect number of 1.5. In yetanother instance, the plurality of heat exchange elements may be diamondshaped pin fins. Further, the pitch corresponding to the plurality ofheat exchange elements may be varied to obtain enhanced heat transfer.For example, the pitch may be varied in proportion to the required heattransfer coefficient.

The surface geometry of the plurality of heat exchange elements may bevaried in order to provide enhanced heat transfer. For instance, squareribs along the plurality of heat exchange elements may be used. Inanother instance, diamond shaped surface protrusions may be providedover the plurality of heat exchange elements. In yet another instance,grooves may be created on the surfaces of the plurality of heat exchangeelements. In a further instance, dimples may be placed on the flat baseof the plurality of heat exchange elements forming a pin fin. Further,in an instance, convex shaped dimples may be used to obtain greater heattransfer.

An orientation of the plurality of heat exchange elements may be variedin order to enhance heat transfer. For instance, in case the number ofthe plurality of heat exchange elements is large, the plurality of heatexchange elements may be oriented vertically with respect to the flatbase of the plurality of heat exchange elements. In another instance, incase the plurality of heat exchange elements are short with a finningfactor of less than 2.7, a horizontal orientation may be used in orderto provide better heat transfer.

The plurality of heat exchange elements may be configured in order tocontrol an amount of heat transfer by radiation. For example, the heightof the plurality of heat exchange elements may be maintained short. Onthe other hand, the height of the plurality of heat exchange elementsmay be increased in order to reduce the amount of heat transfer byradiation. As another example, the plurality of heat exchange elementsmay be circular around an annular heat pipe. Further, a ratio of spacingbetween the plurality of heat exchange elements and diameter of theplurality of heat exchange elements may be controlled in order to varythe amount of heat transfer by radiation. For instance, the ratio may bedecreased in order to decrease the amount of heat transfer by radiation.Similarly, the ratio may be increased in order to increase the amount ofheat transfer by radiation.

The number of iterations corresponding to the fractal variation betweenrespective branches of the plurality of heat exchange elements may beconfigured in order to control heat transfer. For instance, the numberof iterations may be increased in order to obtain greater heat transfer.However, beyond a certain limit, heat transfer may not be directlyproportional to the number of iterations. Additionally, varying thenumber of iterations may also control diffusion rate across the surfacesof the plurality of heat exchange elements based on the fact thatdiffusion rate is directly proportional to the number of iterations.However, a certain number of iterations such as, but not limited to,four to five iterations, the diffusion rate may converge.

A dimension corresponding to the fractal variation between respectivebranches of the plurality of heat exchange elements may be configured inorder to control heat transfer. In general, the heat transfer isdirectly proportional to the fractal dimension. However, thisrelationship is valid only till a limited number of iterations.

The number of branches corresponding to the plurality of heat exchangeelements may be configured to control the heat transfer. Under naturalconvection, heat transfer effectiveness is found to be directlyproportional to the number of branches. However, after a certain numberof branch generations, heat transfer effectiveness saturates. Further, abranching ratio may be configured in order to obtain minimum resistanceto heat conduction and hence greater heat transfer. In a non-limitingexample, a branching ratio of 0.707 (√2/2) or 0.7937 may be used.

As shown in FIGS. 46-48 , a hollow conical perforated structure isprovided, with a set of radially extending branched fins, as a heatsink. According to this design, the branched fins and/or the aperturepattern on the frustum of the hollow conical perorated structure may befractal in nature. A cone is an object having circular cross-sections ofa diminishing radii, self-similar on any scale. The frustum of a hollowcone itself is topologically regular, but the hole pattern may follow afractal pattern. The convection may induce sufficient flows to ensureheat dissipation.

The frustum of a cone rests on a horizontal metal plate that supportsthe whole structure and is attached to the integrated circuit board, thechip or another source of heat that is being cooled. The lower surfaceof the horizontal plate connecting to the surface of the heat source istypically smooth, in order to provide efficient heat transfer from aflat surface of the object from which the heat is received. From thisplate, a cylinder with a diminishing diameter, e.g., a hollow frustum ofa cone, extends, to allow hot air to escape upward (the narrowing of thecylinder is meant to increase the velocity of the air as it rises, topromote the formation of a vortex). As noted above, the perforated holesprove intake of air to create convection. Therefore, the cone angle andhole pattern may be optimized to produce a convective flow over a rangeof operating conditions. This optimization may be performed usingcomputational flow dynamics software.

The surface of the frustum of the hollow cone is perforated with holes,arranged in a pattern, which may be a fractal pattern, to allow air topass through the walls to facilitate the upward draft. An example ofsuch fractal pattern may be spiral arrangement of the holes, wherein thespiral on the surface of a cone is a pattern having diminishing radius,self-similar on any scale. The holes may be arranged in a fractalpattern; note that the chirality and diminishing diameter of the spiralwill tend to make any spatial pattern other than a line of holesasymmetric. The size of the holes may also follow a fractal patterndiminishing with the height of the cone, remaining self-similar on anyscale. The holes provided in a spiral pattern around the cone, maytemplate formation of a vortex. Similarly, the inner surface of the conemay have one or more spiral grooves, to create a helical movement of hotair to promote formation of the vortex. Because of the reversal of theCoriolis effect, designs intended for use below the equator should havea reverse spiral direction.

Heat dissipation elements in the form of fins extend outward of from thefrustum of the cone in a branching pattern, which may be designedaccording to a fractal branching pattern. It is noted that, in somecases, the branching pattern may be defined to deviate from aself-similar fractal branching pattern. For example, where space orother constraints dictate the branching pattern, the result may differfrom a fractal design. The fins may also have a pattern of perforationsand/or surface relief, which may also respectively be provided in afractal pattern.

Such a design may be difficult to produce using a typical subtractivemachining process. However, the design may be produced by an additivemanufacturing process, such as laser sintering or investment castingbased on a three-dimensional printed form. The details or variousparameters of the design may be generated based mechanical and physicalconstraints, a design thesis, and a computational flow dynamicsenvironment, such as Comsol. Design parameters may be iteratedincrementally, using a genetic algorithm, or based on a Monte Carloexploration of the design space, for example. A set of design rules maylimit minimum and maximum feature sizes for various aspects of thedesign.

As shown in FIGS. 46 and 47 , the fins may be provided in an extrudedformation, permitting a composite manufacturing process of thehorizontal place, the conical core and the fins, as separate components,which are connected or fused. Therefore, the materials used for thehorizontal plate, the central core (frustum of a cone), and the finsneed not be identical. For example, the plate may be steel, core may becopper, while the fins may be aluminum.

According to this design, heat dissipation occurs in two ways: (a)formation of the vortex carrying hot air upward away from the base,inside the cylinder or frustum of a cone, and (b) through the outwardlydirected fins carrying heat away from the cylinder or frustum of a cone.Note that the external configuration of the core need not directlycorrelate with the internal configuration, and for example, the externalsurface may be cylindrical and the internal surface may be conical orVenturi-shaped (having a constriction and subsequent dilation).

The perforations on the walls of the cylinder or the frustum of a conemay be optimized for overall efficiency, to enhance peak heatdissipation, or to enhance efficiency at a particular operating point.

A fan or blower may be provided to induce air flow over a range ofspeeds. The design may provide efficient operation using passiveconvective dissipation over a portion of the operating range, and activeheat dissipation over a more extended range. Such a fan may be optimallypositioned on the top of the frustum of a cone over its opening.

Heat transfer may be controlled based on the velocity of fluidic heatexchange medium flowing over the plurality of heat exchange elements. Ingeneral, the heat transfer is directly proportional to the velocity offluidic heat exchange medium under forced convection. Additionally, theoptimal number of branches required to maximize heat transfer has beenfound to reduce with increase in velocity of fluidic heat exchangemedium. Accordingly, under forced convection with higher velocity, lessnumber of branches may be required to achieve a required amount of heattransfer. Heat transfer by the plurality of heat exchange elements inthe form of an array of perforated fins may be controlled by varying apumping power. In this case, the heat transfer can be inverselyproportional to the pumping power with small increase for turbulentcross-flow but significant increase for parallel flow.

Various parts of the heat sink may be manufactured using manufacturingtechniques such as, but not limited to, injection molding, die casting,extrusion, forging, gravitational molding, CNC milling, CNC punching,stamping, wire cut machine and wire cut Electrical Discharge Machining(EDM), additive manufacturing (e.g., 3D printing, 2.5D printing, etc.Various parts of the heat sink may be manufactured by a machiningprocessing employing cutting tools and controlled slicing techniques toconstruct the plurality of heat exchange elements from a solid block ofmaterial such as, but not limited to, copper or aluminum. This techniqueis preferable to construct the plurality of heat exchange elements withsmaller thickness than is possible by other techniques such asextrusion. Advantages of the heat sink manufactured using this techniqueinclude high aspect ratio, thin fin, low tooling cost, easy andinexpensive to prototype, unidirectional flow and single piececonstruction. Parts of the heat sink may also be manufactured by bendingsheets made of, but not limited to, copper or aluminum into fins to formthe plurality of heat exchange elements. The fins are then bonded to theflat base of the heat sink. This technique allows the flat base, thecore, and the fins to be made of different materials. Advantages of thismanufacturing technique include light weight of fins, lower tooling costand differing materials for the flat base and the fins. Various parts ofthe heat sink may be manufactured from sheets of material such as, butnot limited to, copper or aluminum bonded onto the flat base using oneor more of epoxy, soldering and brazing. This technique of manufacturingis suitable for high power application with low thermal resistance andwhere forced air cooling is available. Parts of the heat sink may alsobe manufactured using die casting. In this technique, material such as,but not limited to, liquid aluminum is forced under high pressure intore-usable steel molds. This technique is especially suited when the heatexchange elements are of complex shapes.

Those skilled in the art will recognize many ways to fabricate the heatsinks described herein. For example, modern three-dimensional laser andliquid printers can create objects such as the heat sinks describedherein with a resolution of features on the order of 16 μm. Also, it ispossible to grow a crystal structure using a recursive growth algorithmor through crystal growth techniques. For example, U.S. 2006/0037177,describes a method of controlling crystal growth to produce fractals orother structures through the use of spectral energy patterns byadjusting the temperature, pressure, and electromagnetic energy to whichthe crystal is exposed. This method might be used to fabricate the heatsinks described herein. For larger heat sinks, such as those intended tobe used in car radiators, traditional manufacturing methods for largeequipment can be adapted to create the fractal structures describedherein.

In an extruded multi-level branching heat sink design, the extruded heatsink may be further subject to a spatially varying texturing, which mayresult from deposition or etching. For example, due to the inaccessiblecrevices, a self-assembling/self-organizing etching process ispreferred, in which the approximate surface roughness varies with thetopological distance from the heat source. For example, a solution maybe provided, which deposits particles in a controlled manner. Theparticles in an etch bath are heat activated, and the heat sink isselectively heated such that the particles result in a desireddistribution (size, location, depth) of etched features. Because theseare dependent on the fractal-like shape of the heat sink, they will alsobe fractal. However, interactions between the particles in the etchprocess may also create an independent self-similar spatially varyingresult.

In a typical prior heat sink, the energy cost of a fan is consideredhigh (and the penalty of noise also considered high), and therefore lowpressure and modest heat transfer fluid flow rates are provided, withthe flow tending to be laminar over a set of plates or vanes. Such flowconditions tend to promote particulate deposition on the heat exchangesurfaces. On the other hand, in some cases, the energy cost of the fanand/or noise are not the critical variables to be minimized. In suchcases, high flow rates such as to cause turbulent flow are desirable,since these disrupt the boundary layer and provide a higher heattransfer coefficient, while also reducing (or abating) particulatedeposition on the heat exchange surfaces. In a spatial-filled fractal orfractal-like object has surfaces with characteristic sizes over a broadrange, a heat dissipative structure may be provided in or near thegeometric center. (The structure may be split approximately in half, andthe structure mounted over a heat dissipative structure on a surface).Perforations through the surfaces may be optimized according to amultiscale or fractal algorithm to control cooling medium flow pattern,and heat dissipation. A source of compressed air may be provided blowingin a void near the heat dissipative structure, with the air flow exitingthe structure through the fractal like object. A relatively smallcompressor may pressurize a plenum, which is periodically exhaustedthrough one or more nozzles, toward heat transfer surfaces subject tofouling. The compressor may act in parallel to a fan, i.e., both runconcurrently, and the compressor may be run from the same motor as thefan. The compressor may have at least two modes of operation, oneemployed when the heat dissipation load permits the heat to be shedbased on the fan or convective flows, and therefore permitting theplenum to be charged to relatively high pressures, and thus produce ahigh impulse to dislodge dust and debris, and another mode assumed whenheat load is high, and a more continuous flow of lower pressure air fromthe compressor assist in heat sink operation. In this way, maximum airflow is available at peak heat dissipation requirement times, and alower air flow with high peak flow rates is available at low heatdissipation times. Further, it is noted that vibration of the heatexchange elements of the structure may assist in heat dissipation,especially if movements are macroscopic, and thus are associated withpressure gradients and air flows around the elements.

A heat sink according to the present technology may be designed using acomputational flow dynamics (CFD) model of the heat sink, with either aniterative testing approach with design alternates, for example using agenetic algorithm, or an adaptive deterministic algorithm that is guidedby the CFD properties of the base design. The CFD model may be used asthe optimization criteria for the multiscale generative algorithm. Forexample, the variables of the multiscale generative algorithms for thegross morphology and surface configuration may be initially run in asparse sampling of the entire available parameter range, with the CFDperformance measured for each iteration, over the range of conditions. Agenetic algorithm may then be implemented to further explore thesolution space, using the prior CFD data as guidance. A successcriterion is established, and the search can cease when met, though inmany cases, the cessation criteria is that the design meets theperformance criteria and also that the exploration has consumed budgetedresources, so that a readily findable solution is not unnecessarilyignored. For example, if implemented in a cloud computing environment,the budget may be a cost budget. In other cases, the explorationcontinues for a period of time, and when the deadline passes, the bestsufficient design is employed.

One advantage of this approach is that the optimization may proceed withad hoc constraints, such as spatial constraints. Thus, each iteration ofthe generative algorithm for generating the “shape” fractal (thelower-level design algorithm) presents a choice, which may be guided bythe CFD thermal model of the heat sink. Likewise, the second levelfractal textures may also be designed according to a CFD framework.Because the CFD of the lower level is dependent on the surfaceproperties of the structure, the model for each element (i.e., astructure at a level of recursion of the lower-level algorithm havingthe surface defined by the upper-level texture mapping algorithm)includes properties of both lower and upper levels.

In some cases, the distinct technology may be limited to the secondlevel texture or perforation pattern applied to a basic shape that isdistinct from a fractal design. For example, the texture or perforationpattern may be provided on a symmetric, uniform array (branched orotherwise) of heat sink elements according to known designs.

As discussed above, a presumption of uniform flow of the heat transfermedium is not necessarily applicable, and the design may be optimizedfor a range of flow conditions. For example, as thermal load increases,the flow rate and source vector may change. In some cases, the heat sinkconfiguration itself may change, such as by means of a shape memoryalloy (SMA), bimetallic elements, phase change medium (solid-liquid,liquid gas, etc.), electromagnetic, piezoelectric, etc. Typically, theaddition of additional structure (i.e., mass) to a heat sink leads toincreased efficiency, and for example, a larger branched structure wouldtypically be expected to have greater efficiency than a correspondingheat sink having a smaller branched structure. However, in some cases,the larger structure impairs heat transfer fluid flow, and therefore canlower efficiency.

Typically, the surface texture is provided to increase the efficiency ofthe system at peak heat load, and preferably to reduce cost and/oracoustic emissions at lower loads. Reduced cost includes both materialcost and operating cost, with operating cost typically corresponding tofan running power. Thus, for example, a heat sink design may be modifiedby a surface perforation pattern, and thereby modified to have lowermass and higher surface area, to provide higher peak thermal loadcapacity.

This document describes illustrative examples of the apparatus, methods,and articles of manufacture for making and using fractal heat sinks.Neither the specific embodiments of the invention as a whole, nor thoseof its features necessarily limit the general principles underlying theinvention. The specific features described herein may be used in someembodiments, but not in others, in the various combinations andpermutations, without departure from the spirit and scope of theinvention as set forth herein. Various physical arrangements ofcomponents and various step sequences also fall within the intendedscope of the invention. Many additional modifications are intended inthe foregoing disclosure, and it will be appreciated by those ofordinary skill in the art that in some instances some features of theinvention will be employed in the absence of a corresponding use ofother features. The illustrative examples therefore do not limit themetes and bounds of the invention and the legal protection afforded theinvention, which function is carried out by current and future claimsand their equivalents.

The heat sink may have an associated control system, comprising afeedback input, which may be a system state defining past, present orfuture heat load or other operating conditions, or a feedback sensordefining current temperatures, air flow, acoustic emission (e.g.,indicative of turbulence) or other conditions. The inputs are processedby an automated processor (e.g., microprocessor or microcontroller,and/or a system processor, remote processor (e.g., cloud processor), orthe like. The processor or control system then produces an output, whichmay be used to control a fan or other heat exchange medium flow rate orflow conditions (e.g., a fan speed), a turbulence-generating deviceand/or characteristics thereof (e.g., a distance or orientation of afractal grid from a heat exchange surface), a configuration of a heatexchange surface (e.g., angular inclination with respect to heatexchange medium flow), etc. The algorithm by which the automated controloperates may employ a multifactorial optimization, which may includeenergy consumption of fan or other non-processing components, thermalcycling damage to components, heat damage to components, headroom foradditional processing load, acoustic emissions, processor thermalthrottling, dust accumulation and reduction, and the like. The variousaspects of the operating conditions may be combined into a distancefunction, and treated as a unitary dimensionless variable, or subjectedto a combinatorial optimization, especially where multiple inputs and/oroutputs do not have directly correlated behavior.

What is claimed is:
 1. A heat sink comprising: a body, having anexternal surface, the external surface having an organization defined bya first pattern; at least one physical interface configured toconductively transfer heat with the body; and a flow interactionelement, defined by a second pattern, the second pattern comprising amultiscale self-similar features over a range of at least two differentscales configured to introduce turbulence into a flow of a heat transferfluid interacting with the flow interaction element in at least one flowstate of the heat transfer fluid, wherein a flow pattern of the heattransfer fluid over the body is responsive to the flow state of the heattransfer fluid, the first pattern, and the second pattern.
 2. Theheatsink according to claim 1, wherein the flow interaction elementprecedes a portion of the external surface of the body with respect to aflow path of at least a portion of the heat transfer fluid, such thatthe flow pattern of the at least a portion of the heat transfer fluid ismade turbulent by the second pattern, and the heat transfer fluid havingthe turbulent flow pattern subsequently interacts with the portion ofthe external surface.
 3. The heatsink according to claim 1, wherein theflow interaction element comprises a fractal grid.
 4. The heatsinkaccording to claim 1, wherein the flow interaction element comprises afractal orifice.
 5. The heat sink according to claim 1, wherein the flowinteraction element comprises a 3D fractal filter.
 6. The heat sinkaccording to claim 1, wherein the flow interaction element comprises aplurality of apertures through which the heat transfer fluid flows,before interacting with the portion of the external surface.
 7. Theheatsink according to claim 1, wherein the flow interaction element isprovided on a surface of the body.
 8. The heatsink according to claim 1,wherein the flow interaction element is distinct from the body.
 9. Theheatsink according to claim 1, wherein the body comprises a plurality ofelongated sections separated from each other by void regions, whereinthe void regions are configured as flow paths for the heat transferfluid.
 10. The heat sink according to claim 1, further comprising a fanor blower, configured to induce the flow of the heat transfer fluid. 11.The heat sink according to claim 10, wherein the fan or blower iscontrolled to vary a flow vector of the heat transfer fluid over time toalter a turbulent flow interaction of the heat transfer fluid with theexternal surface according to turbulent flow pattern model of the heattransfer fluid.
 12. The heat sink according to claim 1, wherein thesecond pattern comprises a texture relief pattern on at least a portionof the external surface.
 13. The heat sink according to claim 1, whereinthe second pattern comprises a 3D relief pattern on at least a portionof the external surface.
 14. The heat sink according to claim 1, whereinthe first pattern comprises a multiscale pattern.
 15. The heat sinkaccording to claim 1, wherein the first pattern comprises a multiscalepattern having fractal asymmetries.
 16. The heat sink according to claim1, further comprising: an actuator to control the flow pattern of theheat transfer fluid; and an automated control configured to control theactuator to alter the flow pattern according to at least a spatialturbulence pattern of the heat transfer fluid and a spatial temperaturevariation of the external surface.
 17. A heat sink comprising: anexternal surface of a heat sink body, the external surface having anorganization defined by a first pattern; a conductive heat transfersurface of the heat sink body; a flow interaction element, comprising amultiscale arrangement of length scales and being configured to interactwith a flow of a fluid to generate multiscale turbulence comprisingchaotic motion of the fluid at different length scales; and a flowinducer, configured to generate a flow of the fluid interacting with theflow interaction element to induce the multiscale turbulence in the flowof the flow of the fluid; and an automated control configured to controlthe flow inducer dependent on at least an amount of heat to betransferred through the conductive heat transfer surface, a spatialturbulence pattern of the fluid proximate to the eternal surface, and atemperature variation pattern of the external surface.
 18. A heattransfer method, comprising: providing a heat sink comprising a bodyhaving an external surface organized according to a first pattern and aconductive heat transfer surface, wherein heat is conducted through theheat sink body between the conductive heat transfer surface and theexternal surface, to produce a spatial temperature pattern on theexternal surface; providing a flow interaction element, comprising aplurality of members arranged in a multiscale pattern; and inducing aspatial turbulent flow pattern of a fluid proximate to the externalsurface with the flow interaction element; and automatically controllingthe turbulent flow pattern based on at least an amount of heat to betransferred through the conductive heat transfer surface.
 19. The methodof claim 18, wherein the automatically controlling is further dependenton the spatial turbulence pattern of the fluid proximate to the eternalsurface, and a spatial temperature pattern on the external surface,further comprising at least one of a predictive model for at least oneof the spatial turbulence pattern, and the spatial temperature pattern,and at least one sensor for determining at least one of the spatialturbulence pattern, and the spatial temperature pattern.
 20. The methodaccording to claim 18, wherein the controlling is further dependent onat least one of an acoustic emission, and a power consumed inducing theflow.